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Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 25 - Probability [Latest edition]

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Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 25 - Probability - Shaalaa.com
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Solutions for Chapter 25: Probability

Below listed, you can find solutions for Chapter 25 of CISCE Selina for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई.


EXERCISE 25 (A)EXERCISE 25 (B)TEST YOURSELF
EXERCISE 25 (A) [Pages 399 - 400]

Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई 25 Probability EXERCISE 25 (A) [Pages 399 - 400]

Multiple Choice Type: Choose the correct answer from the options given below.

1. (a)Page 399

If A and B are two complementary events then the relation between P(A) and P(B) is ______.

  • P(A) = P(B)

  • P(A) + P(B) = 0

  • P(A) + P(B) = 1

  • none of these

1. (b)Page 399

Out of the vowels of English alphabet, one letter is selected at random. The probability of selecting the letter ‘O’ is ______.

  • 1

  • \[\frac{4}{5}\]

  • \[\frac{1}{26}\]

  • \[\frac{1}{5}\]

1. (c)Page 399

When a die is thrown, the probability of getting an even number greater than 4 is ______.

  • \[\frac{1}{3}\]

  • \[\frac{2}{3}\]

  • \[\frac{1}{6}\]

  • \[\frac{11}{2}\]

1. (d)Page 399

If a letter is drawn from the letters of English alphabet, then the probability, that it is a letter of the word ‘DELHI’ is ______.

  • \[\frac{1}{5}\]

  • \[\frac{5}{26}\]

  • \[\frac{1}{26}\]

  • \[\frac{21}{26}\]

1. (e)Page 399

A card is selected at random from a well-shuffled deck of 52 cards. The probability of it being a face card is ______.

  • `3/13`

  • `4/13`

  • `6/13`

  • `8/13`

2. (i)Page 399

A coin is tossed once. Find the probability of getting a tail.

2. (ii)Page 399

A coin is tossed once. Find the probability of not getting a tail.

3. (i)Page 399

A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is a black ball.

3. (ii)Page 399

A bag contains 3 white, 5 black, and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is a red ball.

3. (iii)Page 399

A bag contains 3 white, 5 black, and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is a white ball.

3. (iv)Page 399

A bag contains 3 white, 5 black, and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is not a red ball.

3. (v)Page 399

A bag contains 3 white, 5 black, and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is not a black ball.

4. (i)Page 399

In a single throw of a dice, find the probability of getting a number greater than 4.

4. (ii)Page 399

In a single throw of a dice, find the probability of getting a number less than or equal to 4.

4. (iii)Page 399

In a single throw of a dice, find the probability of getting a number not greater than 4.

5. (i)Page 399

From a well-shuffled deck of 52 playing-cards, one card is drawn. Find the probability that the card drawn will be a black card.

5. (ii)Page 399

From a well-shuffled deck of 52 playing-cards, one card is drawn. Find the probability that the card drawn will not be a red card.

5. (iii)Page 399

From a well-shuffled deck of 52 playing-cards, one card is drawn. Find the probability that the card drawn will be a red card.

5. (iv)Page 399

From a well-shuffled deck of 52 playing-cards, one card is drawn. Find the probability that the card drawn will be a face card.

5. (v)Page 399

From a well-shuffled deck of 52 playing-cards, one card is drawn. Find the probability that the card drawn will be a face card of red colour.

6. (i)Page 399

If A and B are two complementary events then what is the relation between P(A) and P(B)?

6. (ii)Page 399

If the probability of happening of an event A is 0.46. What will be the probability of not happening of the event A?

7.Page 399

In a T.T. match between Geeta and Ritu, the probability of the winning of Ritu is 0.73. Find the probability of:

  1. winning of Geeta.
  2. not winning of Ritu.
8.Page 400

In a race between Mahesh and John, the probability that John will lose the race is 0.54. Find the probability of:

  1. winning of Mahesh
  2. winning of John
9. (i)Page 400

Write the probability of a sure event.

9. (ii)Page 400

 Write the probability of an event which is impossible.

9. (iii)Page 400

For an event E, write a relation representing the range of values of P(E).

10. (i)Page 400

In a single throw of a dice, find the probability of getting 5.

10. (ii)Page 400

In a single throw of a dice, find the probability of getting 8.

10. (iii)Page 400

In a single throw of a dice, find the probability of getting a number less than 8.

10. (iv)Page 400

In a single throw of a dice, find the probability of getting a prime number.

11. (i)Page 400

A dice is thrown once. Find the probability of getting an even number.

11. (ii)Page 400

A dice is thrown once. Find the probability of getting a number between 3 and 8.

11. (iii)Page 400

A dice is thrown once. Find the probability of getting an even number or a multiple of 3.

12.Page 400

Which of the following cannot be the probability of an event?

  1. `3/5`
  2. 2.7
  3. 43%
  4. – 0.6
  5. – 3.2
  6. 0.35
13. (i)Page 400

A bag contains six identical black balls. A child withdraws one ball from the bag without looking into it. What is the probability that he takes out a white ball?

13. (ii)Page 400

A bag contains six identical black balls. A child withdraws one ball from the bag without looking into it. What is the probability that he takes out a black ball?

14.Page 400

A single letter is selected at random from the word ‘Probability’. Find the probability that it is a vowel.

15.Page 400

Ramesh chooses a date at random in January for a party. 

 January 
Mon   6 13 20 27
Tue    7 14 21 28
Wed  1 8 15 22 29
Thurs  2 9 16 23 30
Fri  3 10 17 24 31
Sat  4 11 18 25  
Sun  5 12 19 26  

Find the probability that he chooses:  

  1. a Wednesday 
  2. a Friday 
  3. a Tuesday or a Saturday.
EXERCISE 25 (B) [Pages 406 - 407]

Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई 25 Probability EXERCISE 25 (B) [Pages 406 - 407]

Multiple Choice Type: Choose the correct answer from the options given below.

1. (a)Page 406

A card is drawn from a well-shuffled pack of 52 cards. The probability of the card drawn to be king and jack is:

  • 1

  • 0

  • \[\frac{1}{2}\]

  • \[\frac{3}{13}\]

1. (b)Page 406

The probability that a non-leap year has 53 Sundays is ______.

  • 1

  • \[\frac{1}{7}\]

  • \[\frac{1}{365}\]

  • \[\frac{7}{365}\]

1. (c)Page 406

Out of 800 identical articles some are selected and remaining are rejected. If the probability of an article to be rejected is 0·425; the number of rejected articles is ______.

  • 340

  • 800

  • 430

  • 560

1. (d)Page 406

A bag contains 24 balls of which 4 are red, 8 are white and remaining are blue. A ball is drawn at random, the probability of it to be blue is:

  • 0·5

  • 1

  • \[\frac{1}{3}\]

  • 2

1. (e)Page 406

An integer is chosen from integers between 0 and 51, the probability of it to be divisible by 6 is ______.

  • \[\frac{3}{25}\]

  • \[\frac{4}{25}\]

  • \[\frac{1}{50}\]

  • \[\frac{1}{25}\]

2. (i)Page 406

Nine cards (identical in all respects) are numbered 2 to 10. A card is selected from them at random. Find the probability that the card selected will be an even number.

2. (ii)Page 406

Nine cards (identical in all respects) are numbered 2 to 10. A card is selected from them at random. Find the probability that the card selected will be a multiple of 3. 

2. (iii)Page 406

Nine cards (identical in all respects) are numbered 2 to 10. A card is selected from them at random. Find the probability that the card selected will be an even number and a multiple of 3. 

2. (iv)Page 406

Nine cards (identical in all respects) are numbered 2 to 10. A card is selected from them at random. Find the probability that the card selected will be an even number or a multiple of 3.

3. (i)Page 406

Hundred identical cards are numbered from 1 to 100. The cards are well shuffled and then a card is drawn. Find the probability that the number on the card drawn is a multiple of 5.

3. (ii)Page 406

Hundred identical cards are numbered from 1 to 100. The cards are well shuffled and then a card is drawn. Find the probability that the number on the card drawn is a multiple of 6.

3. (iii)Page 406

Hundred identical cards are numbered from 1 to 100. The cards are well shuffled and then a card is drawn. Find the probability that the number on the card drawn is between 40 and 60.

3. (iv)Page 406

Hundred identical cards are numbered from 1 to 100. The cards are well shuffled and then a card is drawn. Find the probability that the number on the card drawn is greater than 85.

3. (v)Page 406

Hundred identical cards are numbered from 1 to 100. The cards are well shuffled and then a card is drawn. Find the probability that the number on the card drawn is less than 48.

4. (i)Page 406

From 25 identical cards, numbered 1, 2, 3, 4, 5, ......, 24, 25; one card is drawn at random. Find the probability that the number on the card drawn is a multiple of 3.

4. (ii)Page 406

From 25 identical cards, numbered 1, 2, 3, 4, 5, ……, 24, 25: one card is drawn at random. Find the probability that the number on the card drawn is a multiple of 5.

4. (iii)Page 406

From 25 identical cards, numbered 1, 2, 3, 4, 5, ......, 24, 25; one card is drawn at random. Find the probability that the number on the card drawn is a multiple of 3 and 5.

4. (iv)Page 406

From 25 identical cards, numbered 1, 2, 3, 4, 5, ......, 24, 25; one card is drawn at random. Find the probability that the number on the card drawn is a multiple of 3 or 5.

5. (i)Page 406

A dice is thrown once. Find the probability of getting a number less than 3.

5. (ii)Page 406

A die is thrown once. Find the probability of getting a number greater than or equal to 4.

5. (iii)Page 406

A dice is thrown once. Find the probability of getting a number less than 8. 

5. (iv)Page 406

A dice is thrown once. Find the probability of getting a number greater than 6.

6.Page 407

A book contains 85 pages. A page is chosen at random. What is the probability that the sum of the digits on the page is 8?

7.Page 407

A pair of dice is thrown. Find the probability of getting a sum of 10 or more, if 5 appears on the first dice.

8. (i)Page 407

If two coins are tossed once, what is the probability of getting both heads.

8. (ii)Page 407

If two coins are tossed once, what is the probability of getting at least one head.

8. (iii)Page 407

If two coins are tossed once, what is the probability of getting both heads or both tails.

9. (i)Page 407

Two dice are rolled together. Find the probability of getting a total of at least 10.

9. (ii)Page 407

Two dice are rolled together. Find the probability of getting a multiple of 2 on one die and an odd number on the other die.

10. (i)Page 407

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is a spade.

10. (ii)Page 407

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is a red card.

10. (iii)Page 407

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is a face card.

10 (iv)Page 407

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is 5 of heart or diamond.

10. (v)Page 407

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is jack or queen.

10. (vi)Page 407

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is ace and king.

10. (vii)Page 407

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is a red and a king.

10. (viii)Page 407

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is a red or a king.

11. (i)Page 407

A bag contains 16 coloured balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is red.

11. (ii)Page 407

A bag contains 16 coloured balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is not red.

11. (iii)Page 407

A bag contains 16 coloured balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is white.

11. (iv)Page 407

A bag contains 16 coloured balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is not white. 

11. (v)Page 407

A bag contains 16 coloured balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is green or red. 

11. (vi)Page 407

A bag contains 16 coloured balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is white or green.

11. (vii)Page 407

A bag contains 16 coloured balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is green or red or white.

12. (i)Page 407

A ball is drawn at random from a box containing 12 white, 16 red and 20 green balls. Determine the probability that the ball drawn is white.

12. (ii)Page 407

A ball is drawn at random from a box containing 12 white, 16 red and 20 green balls. Determine the probability that the ball drawn is red.

12. (iii)Page 407

A ball is drawn at random from a box containing 12 white, 16 red and 20 green balls. Determine the probability that the ball drawn is not green. 

12. (iv)Page 407

A ball is drawn at random from a box containing 12 white, 16 red and 20 green balls. Determine the probability that the ball drawn is red or white.

13. (i)Page 407

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is a red card.

13. (ii)Page 407

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is a black card.

13. (iii)Page 407

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is a spade.

13. (iv)Page 407

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is an ace.

13. (v)Page 407

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is a black ace.

13. (vi)Page 407

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is ace of diamonds.

13. (vii)Page 407

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is not a club.

13. (viii)Page 407

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is a queen or a jack.

14. (i)Page 407

Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is a multiple of 4 or 6.

14. (ii)Page 407

Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is a multiple of 3 and 5. 

14. (iii)Page 407

Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is a multiple of 3 or 5.

15. (i)Page 407

In a single throw of two dice, find the probability of a doublet.

15. (ii)Page 407

In a single throw of two dice, find the probability of a number less than 3 on each dice.

15. (iii)Page 407

In a single throw of two dice, find the probability of an odd number as a sum.

15. (iv)Page 407

In a single throw of two dice, find the probability of a total of at most 10.

15. (v)Page 407

In a single throw of two dice, find the probability of an odd number on one dice and a number less than or equal to 4 on the other dice.   

TEST YOURSELF [Pages 407 - 412]

Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई 25 Probability TEST YOURSELF [Pages 407 - 412]

Multiple Choice Type: Choose the correct answer from the options given below.

1. (a)Page 407

Three coins are tossed simultaneously the probability of getting atleast two heads is ______.

  • \[\frac{1}{2}\]

  • \[\frac{1}{3}\]

  • \[\frac{1}{4}\]

  • \[\frac{3}{8}\]

1. (b)Page 407

A card is drawn from a pack of a well shuffled cards. The probability of getting either a king or a queen is:

  • \[\frac{1}{13}\]

  • \[\frac{2}{13}\]

  • \[\frac{3}{13}\]

  • 0

1. (c)Page 407

Two dice are rolled together and the product (P) of their scores is obtained:

Event A: P is 6. 

Event B: P is an odd number. 

Event C: P is 35.

Which of the following event/events has probability equal to 0?

  • Events B and C

  • Events A and B

  • Event B

  • Event C

1. (d)Page 407

A bag contains 20 red balls, 12 blue balls and 8 green balls. Three balls are drawn one by one with replacement, the probability that the third ball being green is:

  • \[\frac{1}{2}\]

  • \[\frac{2}{5}\]

  • \[\frac{1}{5}\]

  • 1.8

1. (e)Page 408

Below are given the probabilities A, B, C and D of an event. P(A) : `3/5`​, P(B) : 1.2, P(C) : −1.2 and P(D) = `1 2/3`​. Which of the above values of the probabilities is possible:

  • Event A

  • Event B

  • Event C

  • Event D

1. (f)Page 408

A letter of English alphabet is chosen at random from English alphabets.

Assertion (A): The probability that the chosen letter is not a consonant is (5 : 26).

Reason (R): The probability of an event \[=\frac{\text {Total number of outcomes }}{\text { Number of favourable outcomes }}\]

  • A is true, R is false.

  • A is false, R is true.

  • Both A and R are true and R is the correct reason for A.

  • Both A and R are true and R is the incorrect reason for A.

1. (g)Page 408

Number (x) is chosen from −3, −2, −1, 0, 1, 2 and 3. Also, \[x^{2} \leq 5\].

Assertion (A): Probability for \[x^{2} \leq 5\] is \[\frac{3}{7}\].

Reason (R): Probability \[ =\frac{\text { Favourable outcomes }}{\text { Total number of outcomes }}\]

  • A is true, R is false.

  • A is false, R is true.

  • Both A and R are true and R is the correct reason for A.

  • Both A and R are true and R is the incorrect reason for A.

1. (h)Page 408

Face cards of spades are removed from a pack of 52 cards and the remaining cards are well- shuffled. Then a card is drawn from the pack.

Statement (1): The probability of drawing a face card is \[\frac{7}{52}\].

Statement (2): Kings, queens and jacks are the face cards and so the total number of face cards in the pack of 52 cards is 3 × 4 = 12.

  • Both the statements are true.

  • Both the statements are false.

  • Statement 1 is true, and statement 2 is false.

  • Statement 1 is false, and statement 2 is true.

1. (i)Page 408

In a lottery ticket, there are 20 prizes and 25 blanks.

Statement (1): Probability of not getting the prize \[=1-\frac{20}{45}\].

Statement (2): P(getting prize) + P(blank) = 1

  • Both the statements are true.

  • Both the statements are false.

  • Statement 1 is true, and statement 2 is false.

  • Statement 1 is false, and statement 2 is true.

2. (i)Page 408

From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is a face card.

2. (ii)Page 408

From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is not a face card.

2. (iii)Page 408

From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is a queen of black card.

2. (iv)Page 408

From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is a card with number 5 or 6.

2. (v)Page 408

From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is a card with number less than 8.

2. (vi)Page 408

From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is a card with number between 2 and 9.

3. (i)Page 408

In a match between A and B; the probability of winning of A is 0.83. What is the probability of winning of B?

3. (ii)Page 408

In a match between A and B; the probability of losing the match is 0.49 for B. What is the probability of winning of A?

4. (i)Page 408

A and B are friends. Ignoring the leap year, find the probability that both friends will have different birthdays? 

4. (ii)Page 408

A and B are friends. Ignoring the leap year, find the probability that both friends will have the same birthday? 

5. (i)Page 409

A man tosses two different coins (one of Rs 2 and another of Rs 5) simultaneously. What is the probability that he gets at least one head?  

5. (ii)Page 409

A man tosses two different coins (one of Rs 2 and another of Rs 5) simultaneously. What is the probability that he gets at most one head? 

6. (i)Page 409

All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting a black face card. 

6. (ii)Page 409

All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting a queen. 

6. (iii)Page 409

All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting a black card.

7.Page 409

In a musical chairs game, a person has been advised to stop playing the music at any time within 40 seconds after its start. What is the probability that the music will stop within the first 15 seconds?

8. (i)Page 409

In a bundle of 50 shirts, 44 are good, 4 have minor defects and 2 have major defects. What is the probability that it is acceptable to a trader who accepts only a good shirt? 

8. (ii)Page 409

In a bundle of 50 shirts, 44 are good, 4 have minor defects and 2 have major defects. What is the probability that it is acceptable to a trader who rejects only a shirt with major defects?

9. (i)Page 409

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is 8.

9. (ii)Page 409

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is 13. 

9. (iii)Page 407

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is less than or equal to 12.

10.Page 409

The probability that two boys do not have the same birthday is 0.897. What is the probability that the two boys have the same birthday? 

11. (i)Page 409

A bag contains 10 red balls, 16 white balls and 8 green balls. A ball is drawn out of the bag at random. What is the probability that the ball drawn will be not red? 

11. (ii)Page 409

A bag contains 10 red balls, 16 white balls and 8 green balls. A ball is drawn out of the bag at random. What is the probability that the ball drawn will be neither red nor green?

11. (iii)Page 409

A bag contains 10 red balls, 16 white balls and 8 green balls. A ball is drawn out of the bag at random. What is the probability that the ball drawn will be white or green? 

12. (i)Page 409

A bag contains twenty Rs 5 coins, fifty Rs 2 coins and thirty Re 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin will be a Re 1 coin?

12. (ii)Page 409

A bag contains twenty Rs 5 coins, fifty Rs 2 coins and thirty Re 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin will not be a Rs 2 coin? 

12. (iii)Page 409

A bag contains twenty Rs 5 coins, fifty Rs 2 coins and thirty Re 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin will neither be a Rs 5 coin nor be a Re 1 coin?

13.Page 409

A game consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; as shown below.       

 
If the outcomes are equally likely, find the probability that the pointer will point at:

  1. 6
  2. an even number.
  3. a prime number.
  4. a number greater than 8.
  5. a number less than or equal to 9.
  6. a number between 3 and 11.
14. (i)Page 409

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a queen of red color.

14. (ii)Page 409

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a black face card.

14. (iii)Page 409

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting the jack or the queen of the hearts.

14. (iv)Page 409

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a diamond.

14. (v)Page 409

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a diamond or a spade.

15. (i)Page 409

From a deck of 52 cards, all the face cards are removed and then the remaining cards are shuffled. Now one card is drawn from the remaining deck. Find the probability that the card drawn is a black card.

15. (ii)Page 409

From a deck of 52 cards, all the face cards are removed and then the remaining cards are shuffled. Now one card is drawn from the remaining deck. Find the probability that the card drawn is 8 of red color.

15. (iii)Page 409

From a deck of 52 cards, all the face cards are removed and then the remaining cards are shuffled. Now one card is drawn from the remaining deck. Find the probability that the card drawn is a king of black color.  

16. (i)Page 409

Seven cards:- the eight, the nine, the ten, jack, queen, king and ace of diamonds are well shuffled. One card is then picked up at random. 

What is the probability that the card drawn is the eight or the king? 

16. (ii)Page 409

Seven cards:- the eight, the nine, the ten, jack, queen, king and ace of diamonds are well shuffled. One card is then picked up at random. 

 If the king is drawn and put aside, what is the probability that the second card picked up is: 

  1. an ace?
  2. a king?
17. (i)Page 409

4 defective pens are accidentally mixed with 16 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is drawn at random from the lot. What is the probability that the pen is defective?  

17. (ii)Page 409

Suppose the pen drawn in (i) is defective and is not replaced. Now one more pen is drawn at random from the rest. What is the probability that this pen is:

  1. defective
  2. not defective?
18. (i)Page 410

A bag contains 100 identical marble stones which are numbered 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears a perfect square number.

18. (ii)Page 409

A bag contains 100 identical marble stones which are numbered 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears a number divisible by 4.

18. (iii)Page 410

A bag contains 100 identical marble stones which are numbered 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears a number divisible by 5.

18. (iv)Page 410

A bag contains 100 identical marble stones which are numbered 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears a number divisible by 4 or 5.

18. (v)Page 410

A bag contains 100 identical marble stones which are numbered 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears a number divisible by 4 and 5.

19. (i)Page 410

A circle with diameter 20 cm is drawn somewhere on a rectangular piece of paper with length 40 cm and width 30 cm. This paper is kept horizontal on table top and a dice, very small in size, is dropped on the rectangular paper without seeing towards it. If the dice falls and lands on the paper only, find the probability that it will fall and land inside the circle. 

19. (ii)Page 410

A circle with diameter 20 cm is drawn somewhere on a rectangular piece of paper with length 40 cm and width 30 cm. This paper is kept horizontal on table top and a dice, very small in size, is dropped on the rectangular paper without seeing towards it. If the dice falls and lands on the paper only, find the probability that it will fall and land outside the circle.

20. (i)Page 410

Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is 4 or 5. 

20. (ii)Page 410

Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is 7, 8 or 9.

20. (iii)Page 410

Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is between 5 and 8.

20. (iv)Page 410

Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is more than 10.

20. (v)Page 410

Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is less than 6. 

21. (i)Page 410

Three coins are tossed together. Write all the possible outcomes. Now, find the probability of getting exactly two heads.

21. (ii)Page 410

Three coins are tossed together. Write all the possible outcomes. Now, find the probability of getting at least two heads.

21. (iii)Page 410

Three coins are tossed together. Write all the possible outcomes. Now, find the probability of getting at most two heads.

21. (iv)Page 410

Three coins are tossed together. Write all the possible outcomes. Now, find the probability of getting all tails.

21. (v)Page 410

Three coins are tossed together. Write all the possible outcomes. Now, find the probability of getting at least one tail.

22.Page 410

Two dice are thrown simultaneously. What is the probability that: 

  1. 4 will not come up either time?  
  2. 4 will come up at least once?
23. (i)Page 410

Offices in Delhi are open for five days in a week (Monday to Friday). Two employees of an office remain absent for one day in the same particular week. Find the probability that they remain absent on the same day.

23. (ii)Page 410

Offices in Delhi are open for five days in a week (Monday to Friday). Two employees of an office remain absent for one day in the same particular week. Find the probability that they remain absent on consecutive day. 

23. (iii)Page 410

Offices in Delhi are open for five days in a week (Monday to Friday). Two employees of an office remain absent for one day in the same particular week. Find the probability that they remain absent on different days. 

24.Page 410

A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball; find the number of black balls in the box.

25. (i)Page 410

From a pack of 52 playing cards, all cards whose numbers are multiples of 3 are removed. A card is now drawn at random. What is the probability that the card drawn is a face card (King, Jack or Queen). 

25. (ii)Page 410

From a pack of 52 playing cards, all cards whose numbers are multiples of 3 are removed. A card is now drawn at random. What is the probability that the card drawn is an even numbered red card? 

26. (i)Page 410

A die has 6 faces marked by the given numbers as shown below:

1 2 3 – 1 – 2 – 3

The die is thrown once. What is the probability of getting a positive integer?

26. (ii)Page 410

A die has 6 faces marked by the given number as shown below:

1 2 3 –1 –2 –3

The die is thrown once. What is the probability of getting an integer greater than – 3?

26. (iii)Page 410

A die has 6 faces marked by the given numbers as shown below:

1 2 3 – 1 – 2 – 3

The die is thrown once. What is the probability of getting the smallest integer?

27.Page 410

Sixteen cards are labelled as a, b, c, ............... m, n, o, p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is:

  1. a vowel.
  2. a consonant.
  3. none of the letters of the word median.
28.Page 411

A box contains a certain number of balls. On each of 60% balls, letter A is marked. On each of 30% balls, letter B is marked and on each of remaining balls, letter C is marked. A ball is drawn from the box at random. Find the probability that the ball drawn is:

  1. marked C
  2. A or B
  3. neither B nor C
29.Page 411

A box contains a certain number of balls. Some of these balls are marked A, some are marked B and the remaining are marked C. When a ball is drawn at random from the box P(A) = `1/3` and P(B) = `1/4`. If there are 40 balls in the box which are marked C, find the number of balls in the box.

30.Page 411

A die is thrown 300 times and outcomes are noted as given below :

Outcomes 1 2 3 4 5 6
Frequency 50 73 55 44 45 33

When the same die is thrown once more, what is the probability of getting :

  1. 4?
  2. 6?
  3. 5?
  4. 2?
31.Page 411

The percentage of marks obtained by a student of class X in four unit tests are given below :

Unit test I II III IV
Marks secured % 62 69 33 86

A test is selected at random. What is the probability that the student gets 69% marks in the test?

32.Page 411

The following table shows the relationship between the monthly incomes and the number of vehicles in a family. If 2000 families, in a locality, are selected, the information gathered is listed in the table below:

Monthly income (₹) Number of vehicles per family
0 1 2 or more than 1
Less than 10,000 1 140 13
10,000 - 12,000 2 285 17
12,000 - 14,000 0 515 0
14,000 - 16,000 0 449 9
16,000 or more 3 559 7

A family is chosen, write the probability that the family chosen is:

  1. earning ₹ 10,000 - ₹ 12,000 per month and owning exactly 1 (one) vehicle.
  2. earning ₹ 14,000 or more per month and owning 2 or more than 2 vehicles.
  3. not owning more than 1 vehicle.

Case-Study Based Questions:

1.Page 411

A square dartboard has sections numbered from 1 to 12 as shown below. Players have to make a prediction and throw a dart. They win if their dart lands on the section that matches their prediction. Three friends Amit, Aryan and Aman took the challenge.

Based on the above information, answer the following:

  1. What is the probability of Amit winning if he predicted that his dart will land on a prime number?
  2. What is the probability of Aryan winning if he predicted that his dart will land on an odd number?
  3. What is the probability of Aman winning if he predicted that his dart will land on a square number?
  4. Which of the three friends has the highest chance of winning?
2.Page 412

A teacher conducted a survey for 180 students of class 10 for a mathematics project to be given in the class.

She asked the students two MCQ questions, which were "What is their favourite subject?" and "What time do they use their mobile phone at night?". Each student could choose only one option from the choices given below.

The following are the results of the survey conducted:

Mobile phone use Favourite subject
Mathematics Science Computer English
Before 9 pm 20 12 8 4
9 pm - 10 pm 13 15 5 8
10 pm - 11 pm 15 18 6 10
After 11 pm 22 10 6 8

Based on the above information, answer the following questions:

  1. If a student is selected at random, what is the probability that the student uses mobile phone after 11 pm and that their favourite subject is Mathematics?
  2. If a student is selected at random, what is the probability that the student uses mobile phone after 10 pm?
  3. If a student is selected at random, what is the probability that their favourite subject is Science?
  4. If a student is selected at random, what is the probability that the student uses mobile phone before 10 pm and that their favourite subject is either Mathematics or Computer?

Solutions for 25: Probability

EXERCISE 25 (A)EXERCISE 25 (B)TEST YOURSELF
Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 25 - Probability - Shaalaa.com

Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 25 - Probability

Shaalaa.com has the CISCE Mathematics कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई CISCE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. Selina solutions for Mathematics कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई CISCE 25 (Probability) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. Selina textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

Concepts covered in कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 25 Probability are Concept of Probability, Elementary Types of Events and Properties of Probability, Measurement of Probability, Standard Results for Outcomes in Probability, Problems based on Probability, Concept of Probability, Elementary Types of Events and Properties of Probability, Measurement of Probability, Standard Results for Outcomes in Probability, Problems based on Probability, Concept of Probability, Elementary Types of Events and Properties of Probability, Measurement of Probability, Standard Results for Outcomes in Probability, Problems based on Probability.

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Get the free view of Chapter 25, Probability कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई additional questions for Mathematics कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई CISCE, and you can use Shaalaa.com to keep it handy for your exam preparation.

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