#### Chapters

Chapter 2: Polynomials

Chapter 3: Linear Equations in two variables

Chapter 4: Triangles

Chapter 5: Trigonometric Ratios

Chapter 6: T-Ratios of some particular angles

Chapter 7: Trigonometric Ratios of Complementary Angles

Chapter 8: Trigonometric Identities

Chapter 9: Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

Chapter 10: Quadratic Equations

Chapter 11: Arithmetic Progression

Chapter 12: Circles

Chapter 13: Constructions

Chapter 14: Height and Distance

Chapter 15: Probability

Chapter 16: Coordinate Geomentry

Chapter 17: Perimeter and Areas of Plane Figures

Chapter 18: Area of Circle, Sector and Segment

Chapter 19: Volume and Surface Area of Solids

## Chapter 15: Probability

#### RS Aggarwal solutions for Secondary School Class 10 Mathematics Chapter 15 Probability Exercise Exercise 15A [Pages 686 - 689]

**Fill in the blank:**

The probability of an impossible event is ....... .

**Fill in the blank:**

The probability of a sure event is ........ .

**Fill in the blank:**

For any event E, P(E) + P (not E) = ........ .

**Fill in the blank:**

The probability of a possible but not a sure event lies between ......... and ........ .

**Fill in the blank:**

The sum of probabilities of all the outcomes of an experiment is ....... .

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

Two coins are tossed simultaneously. Find the probability of getting exactly 1 head.

Two coins are tossed simultaneously. Find the probability of getting at most 1 headat most 1 head.

Two coins are tossed simultaneously. Find the probability of getting at least 1 head.

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

A die is thrown once. Find the probability of getting a number less than 5.

A die is thrown once. Find the probability of getting a number greater than 2.

A die is thrown once. Find the probability of getting a number between 3 and 6.

A die is thrown once. Find the probability of getting a number other than 3.

A die is thrown once. Find the probability of getting the number 5.

A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.

A child has a die whose 6 faces show the letters given below:

The die is thrown once. What is the probability of getting (i) A and (ii) B?

It is known that a box of 200 electric bulbs contains 16 defective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is defective.

It is known that a box of 200 electric bulbs contains 16 defective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is non-defective.

If the probability of winning a game is 0.7, what is the probability of losing it?

There are 35 students in a class of whom 20 are boys and 15 are girls. From these students one is chosen at random. What is the probability that the chosen student is a boy.

There are 35 students in a class of whom 20 are boys and 15 are girls. From these students one is chosen at random. What is the probability that the chosen student is a girl?

In a lottery there are 10 prizes and 25 blanks. What is the probability of getting a prize?

250 lottery tickets were sold and there are 5 prizes on these tickets. If Kunal has purchased one lottery ticket, what is the probability that he wins a prize?

17 cards numbered 1, 2, 3, 4, .... ,17 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card drawn bears an odd number.

17 cards numbered 1, 2, 3, 4, .... ,17 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card drawn bears a number divisible by 5.

A game of chance consists of spinning an arrow, which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes. Find the probability that the arrow will point at any factor of 8.

In a family of 3 children, find the probability of having at least one boy.

A bag contains 4 white balls, 5 red balls, 2 black balls and 4 green balls. A ball is drawn at random from the bag. Find the probability that it is black.

A bag contains 4 white balls, 5 red balls, 2 black balls and 4 green balls. A ball is drawn at random from the bag. Find the probability that it is not green.

A bag contains 4 white balls, 5 red balls, 2 black balls and 4 green balls. A ball is drawn at random from the bag. Find the probability that it is red or white.

A bag contains 4 white balls, 5 red balls, 2 black balls and 4 green balls. A ball is drawn at random from the bag. Find the probability that it is neither red nor green.

A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of getting a red king,

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

A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that the drawn card is neither a king nor a queen.

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

A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting a black king.

Two different dice are tossed together. Find the probability that the number on each die is even.

Two different dice are tossed together. Find the probability that the sum of the numbers appearing on the two dice is 5.

Two different dice are rolled simultaneously. Find the probability that the sum of the numbers on the two dice is 10.

Two different dice are rolled simultaneously. Find the probability that the sum of the numbers on the two dice is 10.

Two dice are rolled together. Find the probability of getting such numbers on two dice whose product is a perfect square.

Two dice are rolled together. Find the probability of getting such numbers on the two dice whose product is 12.

Cards, marked with numbers 5 to 50, are placed in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card is (i) a prime number less than 10 (ii) a perfect square.

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3,..., 12 as shown in the figure. What is the probability that it will point to 6 ?

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3,..., 12 as shown in the figure. What is the probability that it will point to an even number ?

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3,..., 12 as shown in the figure. What is the probability that it will point to a prime number ?

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3,..., 12 as shown in the figure. What is the probability that it will point to a number which is a multiple of 5?

12 defective pens are accidently mixed with 132 good ones. It is not possible to just look at pen and tell whether or not it is defective. One pen is taken out at random from this lot. Find the probability that the pen taken out is good one.

A lot consists of 144 ballpoint pens of which 20 are defective and others good. Tanvy will buy a pen if it is good, but will not buy it if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that she will buy it,

A lot consists of 144 ballpoint pens of which 20 are defective and others good. Tanvy will buy a pen if it is good, but will not buy it if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that she will not buy it?

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a two-digit number,

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a number divisible by 5.

A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

Suppose the bulb drawn in (i) is not defective and not replaced. Now, bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

A bag contains lemon-flavoured candies only. Hema takes out one candy without looking into the bag. What is the probability that she takes out an orange-flavoured candy ?

A bag contains lemon-flavoured candies only. Hema takes out one candy without looking into the bag. What is the probability that she takes out a lemon-flavoured candy?

There are 40 students in a class of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. He writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of a girl ?

There are 40 students in a class of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. He writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of a boy ?

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing an ace.

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a 4 of spades.

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a 9 of a black suit.

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a red king.

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting a queen.

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

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting a king or an ace.

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting a red ace.

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

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

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

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

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

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

A card is drawn at random form a well-shuffled deck of playing cards. Find the probability that the card drawn is a card of spades of an ace.

A card is drawn at random form a well-shuffled deck of playing cards. Find the probability that the card drawn is a red king.

A card is drawn at random form a well-shuffled deck of playing cards. Find the probability that the card drawn is either a king or a queen.

A card is drawn at random form a well-shuffled deck of playing cards. Find the probability that the card drawn is neither a king nor a queen.

#### RS Aggarwal solutions for Secondary School Class 10 Mathematics Chapter 15 Probability Exercise Exercise 15B [Pages 696 - 699]

A box contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is divisible by 2 or 3.

A box contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is a prime number.

A box contains cards numbered 3, 5, 7, 9, .... , 35, 37. A card is drawn at random from the box. Find the probability that the number on the card is a prime number.

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from the bag. Find the probability that the number on the drawn card is not divisible by 3,

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from the bag. Find the probability that the number on the drawn card is a prime number greater than 7.

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from the bag. Find the probability that the number on the drawn card is not a perfect square number.

Cards bearing numbers 1, 3, 5, .... , 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing a prime number less than 15,

Cards bearing numbers 1, 3, 5, .... , 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing a number divisible by 3 and 5.

A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box, find the probability that it bears a one-digit number,

A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box, find the probability that it bears a number divisible by 5.

A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box, find the probability that it bears an odd number less than 30.

A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box, find the probability that it bears a composite number between 50 and 70.

Cards marked with numbers 1, 3, 5, ..., 101 are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that the number on the drawn card is less than 19.

Cards marked with numbers 1, 3, 5, ..., 101 are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that the number on the drawn card is a prime number less than 20.

Tickets numbered 2, 3, 4, 5, ..., 100, 101 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is an even number.

Tickets numbered 2, 3, 4, 5, ..., 100, 101 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is a number less than 16.

Tickets numbered 2, 3, 4, 5, ..., 100, 101 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is a number which is a perfect square.

Tickets numbered 2, 3, 4, 5, ..., 100, 101 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is a prime number less than 40.

A box contains 80 discs, which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.

A piggy bank contains hundred 50 p coins, seventy ₹1 coin, fifty ₹2 coins and thirty ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will be a ₹1 coin?

A piggy bank contains hundred 50 p coins, seventy ₹1 coin, fifty ₹2 coins and thirty ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will not be a ₹5 coin?

A piggy bank contains hundred 50 p coins, seventy ₹1 coin, fifty ₹2 coins and thirty ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will be a 50 p or a ₹2 coin?

The probability of selecting a red ball at random from the jar that contains only red, blue and orange balls is `1/4`. The probability of selecting a blue ball at random from the same jar is `1/3`. If the jar contains 10 orange balls, find the total number of balls in the jar.

A bag contains 18 balls out of which x balls are red. If the ball is drawn at random from the bag, what is the probability that it is not red?

A bag contains 18 balls out of which x balls are red. If two more red balls are put in the bag, the probability of drawing a red ball will be `9/8` times the probability of drawing a red ball in the first case. Find the value of x.

A jar contains 24 marbles. Some of these are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is `2/3`. Find the number of blue marbles in the jar.

A jar contains 54 marbles, each of which some are blue, some are green and some are white. The probability of selecting a blue marble at random is `1/3` and the probability of selecting a green marble at random is `4/9`. How many white marbles does the jar contain?

A carton consists of 100 shirts of which 88 are good and 8 have minor defects. Rohit, a trader, will only accept the shirts which are good. But Kamal, an another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that it is acceptable to Rohit.

A carton consists of 100 shirts of which 88 are good and 8 have minor defects. Rohit, a trader, will only accept the shirts which are good. But Kamal, an another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that it is acceptable to Kamal?

A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is

- extremely patient,
- extremely kind or honest.

Which of the above values you prefer more?

A die is rolled twice. Find the probability that 5 will not come up either time.

A die is rolled twice. Find the probability that 5 will come up exactly one time.

A die is rolled twice. Find the probability that 5 will come up both the times.

Two dice are rolled once. Find the probability of getting such numbers on two dice whose product is a perfect square.

A letter is chosen at random from the letters of the word ASSOCIATION. Find the probability that the chosen letter is a vowel.

A letter is chosen at random from the letters of the word ASSOCIATION. Find the probability that the chosen letter is a consonant.

A letter is chosen at random from the letters of the word ASSOCIATION. Find the probability that the chosen letter is a an S.

Five cards − the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card is then picked up at random. What is the probability that the drawn card is the queeen?

Five cards − the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card is then picked up at random. If the queen is drawn and put aside and a second card is drawn, find the probability that the second card is

- an ace,
- a queen.

A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.

What is the probability that an ordinary year has 53 Mondays?

All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is a red card.

All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is a face card.

All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is a card of clubs.

All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is drawn from it. Find the probability that the drawn card is a black face card.

All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is drawn from it. Find the probability that the drawn card is a red card.

A game consists of tossing a one-rupee coin three times, and noting its outcome each time. Find the probability of getting three heads.

A game consists of tossing a one-rupee coin three times, and noting its outcome each time. Find the probability of getting at least two tails.

Find the probability that a leap year selected at random will contain 53 Sundays.

#### RS Aggarwal solutions for Secondary School Class 10 Mathematics Chapter 15 Probability Exercise Multiple choice Questions [Pages 705 - 709]

If P(E) denotes the probability of an event E then

P(E) < 0

P(E) > 1

0 ≤ P(E) ≤ 1

−1 ≤ P(E) ≤ 1

If the probability of occurence of an event is p then the probability of non-happening of this event is (p − 1).

(p − 1)

(1 − p)

p

`(1- 1/P)`

What is the probability of an impossible event?

`1/2`

0

1

none of these

What is the probability of a sure event?

0

`1/2`

1

none of these

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

1.5

`3/5`

25%

0.3

A number is selected at random from the numbers 1 to 30. What is the probability that the selected number is a prime number?

`2/3`

`1/6`

`1/3`

`11/30`

The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is

`4/15`

`2/15`

`1/5`

`1/3`

A box conatins cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square is

`1/45`

`2/15`

`4/45`

`1/9`

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears prime number less than 23 is

`7/90`

`1/9`

`4/15`

`8/89`

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears prime number less than 23 is

`1/2`

`2/5`

`3/10`

`5/9`

One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number, which is a multiple of 7, is

`1/7`

`1/8`

`1/5`

`7/40`

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

`1/3`

`0.3`

33%

`7/6`

If the probability of winning a game is 0.4, the probability of losing it is

0.96

`1/0.4`

`0.6`

none of these

If an event cannot occur then its probability is

1

`1/2`

`3/4`

0

There are 20 tickets numbered as 1, 2, 3,..., 20 respectively. One ticket is drawn at random. What is the probability that the number on the ticket drawn is a multiple of 5?

`1/4`

`1/5`

`2/5`

`3/10`

There are 25 tickets numbered 1, 2, 3, 4,..., 25 respectively. One ticket is draw at random. What is the probability that the number on the ticket is a multiple of 3 or 5?

`2/5`

`11/25`

`12/25`

`13/25`

Cards, each marked with one of the numbers 6, 7, 8,..., 15, are placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the probability of getting a card with a number less than 10?

`3/5`

`1/3`

`1/2`

`2/5`

A die is thrown once. The probability of getting an even number is

`1/2`

`1/3`

`1/6`

`5/6`

The probability of throwing a number greater than 2 with a fair die is

`2/5`

`5/6`

`1/3`

`2/3`

A die is thrown once. The probability of getting an odd number greater than 3 is

`1/3`

`1/6`

`1/2````

A die is thrown once. The probability of getting a prime number is

Two dice are thrown together. The probability of getting the same number on the both dice is

`1/2`

`1/3`

`1/6`

`1/12`

The probability of getting 2 heads, when two coins are tossed, is

1

`3/4`

`1/2`

`1/4`

Two dice are thrown simultaneously. What is the probability of getting a doublet?

`1/36`

`5/12`

`1/6`

`2/3`

Two coins are tossed simultaneously. What is the probability of getting at most one head?

`1/4`

`1/2`

`2/3`

`3/4`

Three coins are tossed simultaneously. What is the probability of getting exactly two heads?

`1/2`

`1/4`

`3/8`

`3/4`

In a lottery, there are 8 prizes and 16 blanks. What is the probability of getting a prize?

`1/2`

`1/3`

`2/3`

none of these

In a lottery, there are 6 prizes and 24 blanks. What is the probability of not getting a prize?

`3/4`

`3/5`

`4/5`

none of these

A box contains 3 blue, 2 white and 4 red marbles. If a marbles. If a marble is drawn at random from the box, what is the probability that it will not be a white marble?

`1/3`

`4/9`

`7/9`

`2/9`

A bag contains 4 red and 6 black balls. A ball is taken out of the bag at random. What is the probability of getting a black ball?

`2/5`

`3/5`

`1/10`

none of these

A bag contains 8 red, 2 black and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is not black?

`18/15`

`2/15`

`13/15`

`1/3`

A bag contains 3 white, 4 red and 5 black balls. One ball is drawn at random. What is the probability that the ball drawn is neither black nor white?

`1/4`

`1/2`

`1/3`

`3/4`

A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a black king?

`1/13`

`1/26`

`2/39`

none of these

From a well-shuffled deck of 52 cards, one card is drawn at random. What is the probability of getting a queen?

`1/13`

`1/26`

`4/39`

none of these

One card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a face card?

`1/26`

`3/26`

`3/13`

`4/13`

Once card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a black face card?

`1/26`

`3/26`

`3/13`

`3/14`

One card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a 6?

`3/26`

`1/52`

`1/13`

none of these

## Chapter 15: Probability

## RS Aggarwal solutions for Secondary School Class 10 Mathematics chapter 15 - Probability

RS Aggarwal solutions for Secondary School Class 10 Mathematics chapter 15 (Probability) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Secondary School Class 10 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Secondary School Class 10 Mathematics chapter 15 Probability are Sample Space, Concept Or Properties of Probability, Simple Problems on Single Events, Introduction to Probability, Probability - A Theoretical Approach, Probability Examples and Solutions, Sample Space, Concept Or Properties of Probability, Simple Problems on Single Events, Introduction to Probability, Probability - A Theoretical Approach, Probability Examples and Solutions.

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