# NCERT Solutions for Class 9 Maths Unit 15

## Probability Class 9

### Unit 15 Probability Exercise 15.1 Solutions

Probability is the study of chance or the likelihood of an event happening. Directly or indirectly, probability plays a role in all activities.

For example, we may say that it will probably rain today because most of the days we have observed were rainy days. However, in mathematics, we would require a more accurate way of measuring probability.
Problem : A spinner has 4 equal sectors colored yellow, blue, green and red. What are the chances of landing on blue after spinning the spinner? What are the chances of landing on red?
Solution : The chances of landing on blue are 1 in 4, or one fourth.
The chances of landing on red are 1 in 4, or one fourth.

### Exercise 15.1 : Solutions of Questions on Page Number : 283

Q1 :

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.

Answer :

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

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Q2 :

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.

Answer :

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.

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Q3 :

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.

Answer :

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Q4 :

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

 Outcome 3 heads 2 heads 1 head No head Frequency 23 72 77 28

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

Answer :

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Q5 :

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:

 Monthly income (in Rs) Vehicles per family 0 1 2 Above 2 Less than 7000 10 160 25 0 7000 - 10000 0 305 27 2 10000 - 13000 1 535 29 1 13000 - 16000 2 469 59 25 160

Answer :

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Q6 :

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.

Answer :

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Q7 :

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

Answer :

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Q8 :

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?

Answer :

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Q9 :

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.

Answer :

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Q10 :
 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.

Answer :

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Q11 :
 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.

Answer :

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Maths : CBSE NCERT Exercise Solutions for Class 9th for Probability ( Exercise 15.1 ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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 Exercise 15.1 Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11