# 15-PROBABILITY

Here we are going through the ncert solutions for class 9 maths chapter 15– probability so before going through the ncert solutions make sure to go through the textbook that helps you to understand the solutions more easily

## (ncert solutions for class 9 maths chapter 15)

Question 1:

In a cricket math, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

Number of times the batswoman hits a boundary = 6

Total number of balls played = 30

∴ Number of times that the batswoman does not hit a boundary = 30 − 6 = 24

Question 2:

1500 families with 2 children were selected randomly, and the following data were recorded:

 Number of girls in a family 2 1 0 Number of families 475 814 211

Compute the probability of a family, chosen at random, having

(i) 2 girls (ii) 1 girl (iii) No girl

Also check whether the sum of these probabilities is 1.

Total number of families = 475 + 814 + 211

= 1500

(i) Number of families having 2 girls = 475

(ii) Number of families having 1 girl = 814

(iii) Number of families having no girl = 211

Therefore, the sum of all these probabilities is 1.

Question 3:                                                  (ncert solutions for class 9 maths chapter 15)

In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained:

Find the probability that a student of the class was born in August.

Number of students born in the month of August = 6

Total number of students = 40

Question 4:                                          (ncert solutions for class 9 maths chapter 15)

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

Number of times 2 heads come up = 72

Total number of times the coins were tossed = 200

Question 5:

An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:

Suppose a family is chosen, find the probability that the family chosen is

(i) earning Rs 10000 − 13000 per month and owning exactly 2 vehicles.

(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.

(iii) earning less than Rs 7000 per month and does not own any vehicle.

(iv) earning Rs 13000 − 16000 per month and owning more than 2 vehicles.

(v) owning not more than 1 vehicle.

Number of total families surveyed = 10 + 160 + 25 + 0 + 0 + 305 + 27 + 2 + 1 + 535 + 29 + 1 + 2 + 469 + 59 + 25 + 1 + 579 + 82 + 88 = 2400

(i) Number of families earning Rs 10000 − 13000 per month and owning exactly 2 vehicles = 29

Hence, required probability,

(ii) Number of families earning Rs 16000 or more per month and owning exactly 1 vehicle = 579

Hence, required probability,

(iii) Number of families earning less than Rs 7000 per month and does not own any vehicle = 10

Hence, required probability,

(iv) Number of families earning Rs 13000 − 16000 per month and owning more than 2 vehicles = 25

Hence, required probability,

(v) Number of families owning not more than 1 vehicle = 10 + 160 + 0 + 305 + 1 + 535 + 2 + 469 + 1 + 579 = 2062

Hence, required probability,

Question 6:                                              (ncert solutions for class 9 maths chapter 15)

A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 − 20, 20 − 30… 60 − 70, 70 − 100. Then she formed the following table:

 Marks Number of student 0 − 20   20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − above 7   10 10 20 20 15 8 Total 90

(i) Find the probability that a student obtained less than 20 % in the mathematics test.

(ii) Find the probability that a student obtained marks 60 or above.

Totalnumber of students = 90

(i) Number of students getting less than 20 % marks in the test = 7

Hence, required probability,

(ii) Number of students obtaining marks 60 or above = 15 + 8 = 23

Hence, required probability,

Question 7:

To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table.

 Opinion Number of students like   dislike 135   65

Find the probability that a student chosen at random

(i) likes statistics, (ii) does not like it

Total number of students = 135 + 65 = 200

(i) Number of students liking statistics = 135

(ii) Number of students who do not like statistics = 65

Question 8:                                            (ncert solutions for class 9 maths chapter 15)

The distance (in km) of 40 engineers from their residence to their place of work were found as follows.

 5 3 10 20 25 11 13 7 12 31 19 10 12 17 18 11 32 17 16 2 7 9 7 8 3 5 12 15 18 3 12 14 2 9 6 15 15 7 6 12

What is the empirical probability that an engineer lives:

(i) less than 7 km from her place of work?

(ii) more than or equal to 7 km from her place of work?

(iii) within  km from her place of work?

(i) Total number of engineers = 40

Number of engineers living less than 7 km from their place of work = 9

Hence, required probability that an engineer lives less than 7 km from her place of work,

(ii) Number of engineers living more than or equal to 7 km from their place of work = 40 − 9 = 31

Hence, required probability that an engineer lives more than or equal to 7 km from her place of work,

(iii) Number of engineers living within  km from her place of work = 0

Hence, required probability that an engineer lives within  km from her place of work, P = 0

Question 9:

Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.

This is an activity based question. Students are advised to perform this activity by yourself.

Question 10:                                      (ncert solutions for class 9 maths chapter 15)

Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.

This is an activity based question. Students are advised to perform this activity by yourself.

Question 11:

Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg):

4.97 5.05 5.08 5.03 5.00 5.06 5.08 4.98 5.04 5.07 5.00

Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

Number of total bags = 11

Number of bags containing more than 5 kg of flour = 7

Hence, required probability,

Question 12:

 Concentration of SO2 (in ppm) Number of days (frequency ) 0.00 − 0.04 4 0.04 − 0.08 9 0.08 − 0.12 9 0.12 − 0.16 2 0.16 − 0.20 4 0.20 − 0.24 2 Total 30

The above frequency distribution table represents the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 − 0.16 on any of these days.

Number days for which the concentration of sulphur dioxide was in the interval of 0.12 − 0.16 = 2

Total number of days = 30

Hence, required probability,

Question 13:                                          (ncert solutions for class 9 maths chapter 15)

 Blood group Number of students A 9 B 6 AB 3 O 12 Total 30

The above frequency distribution table represents the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB.