Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board chapter 8 - Statistics and Probability [Latest edition]

## Chapter 8: Statistics and Probability

Exercise 8.1Exercise 8.2Exercise 8.3Exercise 8.4Exercise 8.5Unit Exercise – 8
Exercise 8.1 [Pages 313 - 314]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 8 Statistics and Probability Exercise 8.1 [Pages 313 - 314]

Exercise 8.1 | Q 1. (i) | Page 313

Find the range and coefficient of range of the following data

63, 89, 98, 125, 79, 108, 117, 68

Exercise 8.1 | Q 1. (ii) | Page 313

Find the range and coefficient of range of the following data

43.5, 13.6, 18.9, 38.4, 61.4, 29.8

Exercise 8.1 | Q 2 | Page 313

If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value

Exercise 8.1 | Q 3 | Page 313

Calculate the range of the following data.

 Income 400 − 450 450 − 500 500 − 550 550 − 600 600 − 650 Number of workers 8 12 30 21 6
Exercise 8.1 | Q 4 | Page 313

A teacher asked the students to complete 60 pages of a record notebook. Eight students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation of the pages yet to be completed by them.

Exercise 8.1 | Q 5 | Page 313

Find the variance and standard deviation of the wages of 9 workers given below:

₹ 310, ₹ 290, ₹ 320, ₹ 280, ₹ 300, ₹ 290, ₹ 320, ₹ 310, ₹ 280

Exercise 8.1 | Q 6 | Page 313

A wall clock strikes the bell once at 1 o’clock, 2 times at 2 o’clock, 3 times at 3 o’clock and so on. How many times will it strike in a particular day? Find the standard deviation of the number of strikes the bell make a day.

Exercise 8.1 | Q 7 | Page 313

Find the standard deviation of the first 21 natural numbers.

Exercise 8.1 | Q 8 | Page 313

If the standard deviation of a data is 4.5 and if each value of the data is decreased by 5, then find the new standard deviation

Exercise 8.1 | Q 9 | Page 313

If the standard deviation of a data is 3.6 and each value of the data is divided by 3, then find the new variance and new standard deviation

Exercise 8.1 | Q 10 | Page 313

The rainfall recorded in various places of five districts in a week are given below. Find its standard deviation

 Rainfall (in mm) 45 50 55 60 65 70 Number of places 5 13 4 9 5 4
Exercise 8.1 | Q 11 | Page 314

In a study about viral fever, the number of people affected in a town were noted as Find its standard deviation

 Age in years 0−10 10−20 20−30 30−40 40−50 50−60 60−70 Number of people affected 3 5 16 18 12 7 4
Exercise 8.1 | Q 12 | Page 314

The measurements of the diameters (in cms) of the plates prepared in a factory are given below. Find the standard deviation

 Diameter (cm) 21 − 24 25 − 28 29 − 32 33 − 36 37 − 40 41 − 44 Number of plates 15 18 20 16 8 7
Exercise 8.1 | Q 13 | Page 314

The time taken by 50 students to complete a 100-meter race are given below. Find its standard deviation

 Time taken (sec) 8.5 − 9.5 9.5 − 10.5 10.5 − 11.5 11.5 − 12.5 12.5 − 13.5 Number of students 6 8 17 10 9
Exercise 8.1 | Q 14 | Page 314

For a group of 100 candidates, the mean and standard deviation of their marks were found to be 60 and 15 respectively. Later on, it was found that the scores 45 and 72 were wrongly entered as 40 and 27. Find the correct mean and standard deviation

Exercise 8.1 | Q 15 | Page 314

The mean and variance of seven observations are 8 and 16 respectively. If five of these are 2, 4, 10, 12 and 14, then find the remaining two observations.

Exercise 8.2 [Page 316]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 8 Statistics and Probability Exercise 8.2 [Page 316]

Exercise 8.2 | Q 1 | Page 316

The standard deviation and mean of a data are 6.5 and 12.5 respectively. Find the coefficient of variation.

Exercise 8.2 | Q 2 | Page 316

The standard deviation and coefficient of variation of a data are 1.2 and 25.6 respectively. Find the value of mean.

Exercise 8.2 | Q 3 | Page 316

If the mean and coefficient of variation of a data are 15 and 48 respectively, then find the value of standard deviation.

Exercise 8.2 | Q 4 | Page 316

If n = 5, bar(x) = 6, sumx^2 = 765, then calculate the coefficient of variation.

Exercise 8.2 | Q 5 | Page 316

Find the coefficient of variation of 24, 26, 33, 37, 29, 31.

Exercise 8.2 | Q 6 | Page 316

The time taken (in minutes) to complete a homework by 8 students in a day are given by 38, 40, 47, 44, 46, 43, 49, 53. Find the coefficient of variation.

Exercise 8.2 | Q 7 | Page 316

The total marks scored by two students Sathya and Vidhya in 5 subjects are 460 and 480 with standard deviation of 4.6 and 2.4 respectively. Who is more consistent in performance?

Exercise 8.2 | Q 8 | Page 316

The mean and standard deviation of marks obtained by 40 students of a class in three subjects Mathematics, Science and Social Science are given below

 Subject Mean SD Mathematics 56 12 Science 65 14 Social Science 60 10

Which of the three subjects shows more consistent and which shows less consistent in marks?

Exercise 8.3 [Pages 323 - 324]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 8 Statistics and Probability Exercise 8.3 [Pages 323 - 324]

Exercise 8.3 | Q 1 | Page 323

Write the sample space for tossing three coins using tree diagram

Exercise 8.3 | Q 2 | Page 323

Write the sample space for selecting two balls from a bag containing 6 balls numbered 1 to 6 (using tree diagram)

Exercise 8.3 | Q 3. (i) | Page 323

If A is an event of a random experiment such that "P"("A"):"P"(bar"A") = 17 : 15 and n(S) = 640 then find "P"(bar"A")

Exercise 8.3 | Q 3. (ii) | Page 323

If A is an event of a random experiment such that "P"("A") : "P"(bar"A") = 17 : 15 and n(S) = 640 then find n(A)

Exercise 8.3 | Q 4 | Page 323

A coin is tossed thrice. What is the probability of getting two consecutive tails?

Exercise 8.3 | Q 5. (i) | Page 323

At a fete, cards bearing numbers 1 to 1000, one number on one card are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square number greater than 500, the player wins a prize. What is the probability that the first player wins a prize?

Exercise 8.3 | Q 5. (ii) | Page 323

At a fete, cards bearing numbers 1 to 1000, one number on one card are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square number greater than 500, the player wins a prize. What is the probability that the second player wins a prize if the first has won?

Exercise 8.3 | Q 6. (i) | Page 323

A bag contains 12 blue balls and x red balls. If one ball is drawn at random what is the probability that it will be a red ball?

Exercise 8.3 | Q 6. (ii) | Page 323

A bag contains 12 blue balls and x red balls. If one ball is drawn at random if 8 more red balls are put in the bag, and if the probability of drawing a red ball will be twice that it will be a red ball, then find x.

Exercise 8.3 | Q 7. (i) | Page 323

Two unbiased dice are rolled once. Find the probability of getting a doublet (equal numbers on both dice)

Exercise 8.3 | Q 7. (ii) | Page 323

Two unbiased dice are rolled once. Find the probability of getting the product as a prime number

Exercise 8.3 | Q 7. (iii) | Page 323

Two unbiased dice are rolled once. Find the probability of getting the sum as a prime number

Exercise 8.3 | Q 7. (iv) | Page 323

Two unbiased dice are rolled once. Find the probability of getting the sum as 1

Exercise 8.3 | Q 8. (i) | Page 324

Three fair coins are tossed together. Find the probability of getting all heads

Exercise 8.3 | Q 8. (ii) | Page 324

Three fair coins are tossed together. Find the probability of getting atleast one tail

Exercise 8.3 | Q 8. (iii) | Page 324

Three fair coins are tossed together. Find the probability of getting atmost one head

Exercise 8.3 | Q 8. (iv) | Page 324

Three fair coins are tossed together. Find the probability of getting atmost two tails

Exercise 8.3 | Q 9. (i) | Page 324

A bag contains 5 red balls, 6 white balls, 7 green balls, 8 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is white

Exercise 8.3 | Q 9. (ii) | Page 324

A bag contains 5 red balls, 6 white balls, 7 green balls, 8 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is black or red

Exercise 8.3 | Q 9. (iii) | Page 324

A bag contains 5 red balls, 6 white balls, 7 green balls, 8 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is not white

Exercise 8.3 | Q 9. (iv) | Page 324

A bag contains 5 red balls, 6 white balls, 7 green balls, 8 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is neither white or black

Exercise 8.3 | Q 10 | Page 324

In a box there are 20 non-defective and some defective bulbs. If the probability that a bulb selected at random from the box found to be defective is 3/8 then, find the number of defective bulbs

Exercise 8.3 | Q 11. (i) | Page 324

The king and queen of diamonds, queen and jack of hearts, jack and king of spades are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is a clavor

Exercise 8.3 | Q 11. (ii) | Page 324

The king and queen of diamonds, queen and jack of hearts, jack and king of spades are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is a queen of red card

Exercise 8.3 | Q 11. (iii) | Page 324

The king and queen of diamonds, queen and jack of hearts, jack and king of spades are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is a king of black card

Exercise 8.3 | Q 12 | Page 324

Some boys are playing a game, in which the stone thrown by them landing in a circular region is considered as win and landing other than the circular region is considered as a loss. What is the probability to win the game? (π = 3.14)

Exercise 8.3 | Q 13. (i) | Page 324

Two customers Priya and Amuthan are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another day. What is the probability that both will visit the shop on the same day?

Exercise 8.3 | Q 13. (ii) | Page 324

Two customers Priya and Amuthan are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another day. What is the probability that both will visit the shop on different days?

Exercise 8.3 | Q 13. (iii) | Page 324

Two customers Priya and Amuthan are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another day. What is the probability that both will visit the shop on consecutive days?

Exercise 8.3 | Q 14. (i) | Page 324

In a game, the entry fee is ₹ 150. The game consists of tossing a coin 3 times. Dhana bought a ticket for entry. If one or two heads show, she gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise, she will lose. Find the probability that she gets double entry fee

Exercise 8.3 | Q 14. (ii) | Page 324

In a game, the entry fee is ₹ 150. The game consists of tossing a coin 3 times. Dhana bought a ticket for entry. If one or two heads show, she gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise, she will lose. Find the probability that she just gets her entry fee

Exercise 8.3 | Q 14. (iii) | Page 324

In a game, the entry fee is ₹ 150. The game consists of tossing a coin 3 times. Dhana bought a ticket for entry. If one or two heads show, she gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise, she will lose. Find the probability that she loses the entry fee

Exercise 8.4 [Page 330]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 8 Statistics and Probability Exercise 8.4 [Page 330]

Exercise 8.4 | Q 1 | Page 330

If P(A) = 2/3, P(B) = 2/5, P(A ∪ B) = 1/3, then find P(A ∩ B)

Exercise 8.4 | Q 2. (i) | Page 330

A and B are two events such that, P(A) = 0.42, P(B) = 0.48, and P(A ∩ B) = 0.16. Find P(not A)

Exercise 8.4 | Q 2. (ii) | Page 330

A and B are two events such that, P(A) = 0.42, P(B) = 0.48, and P(A ∩ B) = 0.16. Find P(not B)

Exercise 8.4 | Q 2. (iii) | Page 330

A and B are two events such that, P(A) = 0.42, P(B) = 0.48, and P(A ∩ B) = 0.16. Find P(A or B)

Exercise 8.4 | Q 3 | Page 330

If A and B are two mutually exclusive events of a random experiment and P(not A) = 0.45, P(A ∪ B) = 0.65, then find P(B).

Exercise 8.4 | Q 4 | Page 330

The probability that atleast one of A and B occur is 0.6. If A and B occur simultaneously with probability 0.2, then find "P"(bar"A") + "P"(bar"B")

Exercise 8.4 | Q 5 | Page 330

The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then find the probability of neither A nor B happen

Exercise 8.4 | Q 6 | Page 330

Two dice are rolled once. Find the probability of getting an even number on the first die or a total of face sum 8.

Exercise 8.4 | Q 7 | Page 330

From a well-shuffled pack of 52 cards, a card is drawn at random. Find the probability of its being either a red king or a black queen

Exercise 8.4 | Q 8 | Page 330

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 drawn card have either multiples of 7 or a prime number.

Exercise 8.4 | Q 9 | Page 330

Three unbiased coins are tossed once. Find the probability of getting atmost 2 tails or atleast 2 heads

Exercise 8.4 | Q 10 | Page 330

The probability that a person will get an electrification contract is 3/5 and the probability that he will not get plumbing contract is 5/8. The probability of getting atleast one contract is 5/7. What is the probability that he will get both?

Exercise 8.4 | Q 11 | Page 330

In a town of 8000 people, 1300 are over 50 years and 3000 are females. It is known that 30% of the females are over 50 years. What is the probability that a chosen individual from the town is either a female or over 50 years?

Exercise 8.4 | Q 12 | Page 330

A coin is tossed thrice. Find the probability of getting exactly two heads or atleast one tail or two consecutive heads

Exercise 8.4 | Q 13 | Page 330

If A, B, C are any three events such that probability of B is twice as that of probability of A and probability of C is thrice as that of probability of A and if P(A ∩ B) = 1/6, P(B ∩ C) = 1/4, P(A ∩ C) = 1/8, P(A ∪ B ∪ C) = 9/10 and P(A ∩ B ∩ C) = 1/15, then find P(A), P(B) and P(C)

Exercise 8.4 | Q 14 | Page 330

In a class of 35, students are numbered from 1 to 35. The ratio of boys to girls is 4 : 3. The roll numbers of students begin with boys and end with girls. Find the probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number.

Exercise 8.5 [Pages 331 - 332]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 8 Statistics and Probability Exercise 8.5 [Pages 331 - 332]

#### Multiple Choice Questions

Exercise 8.5 | Q 1 | Page 331

Which of the following is not a measure of dispersion?

• Range

• Standard deviation

• Arithmetic mean

• Variance

Exercise 8.5 | Q 2 | Page 331

The range of the data 8, 8, 8, 8, 8 ........ 8 is

• 0

• 1

• 8

• 3

Exercise 8.5 | Q 3 | Page 331

The sum of all deviations of the data from its mean is

• always positive

• always negative

• zero

• non-zero integer

Exercise 8.5 | Q 4 | Page 331

The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all deviations is

• 40000

• 160900

• 160000

• 30000

Exercise 8.5 | Q 5 | Page 331

Variance of first 20 natural numbers is

• 32.25

• 44.25

• 33.25

• 30

Exercise 8.5 | Q 6 | Page 331

The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is

• 3

• 15

• 5

• 225

Exercise 8.5 | Q 7 | Page 331

If the standard deviation of x, y, z is p then the standard deviation of 3x + 5, 3y + 5, 3z + 5 is

• 3p + 5

• 3p

• p + 5

• 9p + 15

Exercise 8.5 | Q 8 | Page 331

If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is

• 3.5

• 3

• 4.5

• 2.5

Exercise 8.5 | Q 9 | Page 331

Which of the following is incorrect?

• P(A) > 1

• 0 ≤ P(A) ≤ 1

• P(Φ) = 0

• "P"("A") + "P"(bar"A") = 1

Exercise 8.5 | Q 10 | Page 331

The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

• "q"/("p" + "q" + "r")

• "p"/("p" + "q" + "r")

• ("p" + "q")/("p" + "q" + "r")

• ("p" + "r")/("p" + "q" + "r")

Exercise 8.5 | Q 11 | Page 331

A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is

• 3/10

• 7/10

• 3/9

• 7/9

Exercise 8.5 | Q 12 | Page 331

The probability of getting a job for a person is x/3. If the probability of not getting the job is 2/3 then the value of x is

• 2

• 1

• 3

• 1.5

Exercise 8.5 | Q 13 | Page 332

Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is 1/9, then the number of tickets bought by Kamalam is

• 5

• 10

• 15

• 20

Exercise 8.5 | Q 14 | Page 332

If a letter is chosen at random from the English alphabets {a, b, …, z}, then the probability that the letter chosen precedes x

• 12/13

• 1/13

• 23/26

• 3/26

Exercise 8.5 | Q 15 | Page 332

A purse contains 10 notes of ₹ 2000, 15 notes of ₹ 500, and 25 notes of ₹ 200. One note is drawn at random. What is the probability that the note is either a ₹ 500 note or ₹ 200 note?

• 1/5

• 3/10

• 2/3

• 4/5

Unit Exercise – 8 [Pages 332 - 333]

### Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 8 Statistics and Probability Unit Exercise – 8 [Pages 332 - 333]

Unit Exercise – 8 | Q 1 | Page 332

The mean of the following frequency distribution is 62.8 and the sum of all frequencies is 50. Compute the missing frequencies f1 and f2.

 Class Interval 0 − 20 20 − 40 40 − 60 60 − 80 80 − 100 100 − 120 Frequency 5 f1 10 f2 7 8
Unit Exercise – 8 | Q 2 | Page 332

The diameter of circles (in mm) drawn in the design are given below.

 Diameters 33 − 36 37 − 40 41 − 44 45 − 48 49 − 52 Number of circles 15 17 21 22 25

Calculate the standard deviation.

Unit Exercise – 8 | Q 3 | Page 332

The frequency distribution is given below.

 x k 2k 3k 4k 5k 6k f 2 1 1 1 1 1

In the table, k is a positive integer, has a variance of 160. Determine the value of k.

Unit Exercise – 8 | Q 4 | Page 332

The standard deviation of some temperature data in degree Celsius (°C) is 5. If the data were converted into degree Fahrenheit (°F) then what is the variance?

Unit Exercise – 8 | Q 5 | Page 332

If for a distribution, sum(x - 5) = 3, sum(x - 5)^2 = 43, and total number of observations is 18, find the mean and standard deviation

Unit Exercise – 8 | Q 6 | Page 332

Prices of peanut packets in various places of two cities are given below. In which city, prices were more stable?

 Prices in city A 20 22 19 23 16 Prices in city B 10 20 18 12 15
Unit Exercise – 8 | Q 7 | Page 332

If the range and coefficient of range of the data are 20 and 0.2 respectively, then find the largest and smallest values of the data

Unit Exercise – 8 | Q 8 | Page 333

If two dice are rolled, then find the probability of getting the product of face value 6 or the difference of face values 5

Unit Exercise – 8 | Q 9 | Page 333

In a two children family, find the probability that there is at least one girl in a family

Unit Exercise – 8 | Q 10 | Page 333

A bag contains 5 white and some black balls. If the probability of drawing a black ball from the bag is twice the probability of drawing a white ball then find the number of black balls.

Unit Exercise – 8 | Q 11 | Page 333

The probability that a student will pass the final examination in both English and Tamil is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Tamil examination?

Unit Exercise – 8 | Q 12. (i) | Page 333

The King, Queen and Jack of the suit spade are removed from a deck of 52 cards. One card is selected from the remaining cards. Find the probability of getting a diamond

Unit Exercise – 8 | Q 12. (ii) | Page 333

The King, Queen and Jack of the suit spade are removed from a deck of 52 cards. One card is selected from the remaining cards. Find the probability of getting a queen

Unit Exercise – 8 | Q 12. (iii) | Page 333

The King, Queen and Jack of the suit spade are removed from a deck of 52 cards. One card is selected from the remaining cards. Find the probability of getting a spade

Unit Exercise – 8 | Q 12. (iv) | Page 333

The King, Queen and Jack of the suit spade are removed from a deck of 52 cards. One card is selected from the remaining cards. Find the probability of getting a heart card bearing the number 5

## Chapter 8: Statistics and Probability

Exercise 8.1Exercise 8.2Exercise 8.3Exercise 8.4Exercise 8.5Unit Exercise – 8

## Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board chapter 8 - Statistics and Probability

Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board chapter 8 (Statistics and 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 Tamil Nadu Board of Secondary Education Mathematics Class 10 SSLC Tamil Nadu State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Class 10 SSLC Tamil Nadu State Board chapter 8 Statistics and Probability are Introduction of Statistics and Probability, Measures of Dispersion, Coefficient of Variation, Probability, Algebra of Events, Addition Theorem of Probability.

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