#### Chapters

## Chapter 8: Statistics and Probability

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

Find the range and coefficient of range of the following data

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

Find the range and coefficient of range of the following data

43.5, 13.6, 18.9, 38.4, 61.4, 29.8

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

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 |

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.

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

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

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.

Find the standard deviation of the first 21 natural numbers.

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

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

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 |

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 |

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 |

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 |

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

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.

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

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

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

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

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

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

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.

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?

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?

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

Write the sample space for tossing three coins using tree diagram

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

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")`

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)

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

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?

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?

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?

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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?

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?

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?

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

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

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

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

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

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)

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)

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)

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).

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")`

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

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

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

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.

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

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?

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?

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

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)

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.

### 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

Which of the following is not a measure of dispersion?

Range

Standard deviation

Arithmetic mean

Variance

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

0

1

8

3

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

always positive

always negative

zero

non-zero integer

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

Variance of first 20 natural numbers is

32.25

44.25

33.25

30

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

3

15

5

225

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

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

Which of the following is incorrect?

P(A) > 1

0 ≤ P(A) ≤ 1

P(Φ) = 0

`"P"("A") + "P"(bar"A")` = 1

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")`

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`

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

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

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`

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`

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

The mean of the following frequency distribution is 62.8 and the sum of all frequencies is 50. Compute the missing frequencies f_{1} and f_{2}.

Class Interval |
0 − 20 | 20 − 40 | 40 − 60 | 60 − 80 | 80 − 100 | 100 − 120 |

Frequency |
5 | f_{1} |
10 | f_{2} |
7 | 8 |

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.

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.

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?

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

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 |

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

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

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

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.

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?

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

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

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

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

## 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.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Samacheer Kalvi textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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.

Using Samacheer Kalvi Class 10th solutions Statistics and Probability exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Samacheer Kalvi Solutions are important questions that can be asked in the final exam. Maximum students of Tamil Nadu Board of Secondary Education Class 10th prefer Samacheer Kalvi Textbook Solutions to score more in exam.

Get the free view of chapter 8 Statistics and Probability Class 10th extra questions for Mathematics Class 10 SSLC Tamil Nadu State Board and can use Shaalaa.com to keep it handy for your exam preparation