NCERT Solution for Class 9 Mathematics Chapter 15 - Probability RR ACADEMY MEERUT

NCERT Solution for Class 9 Mathematics Chapter 15 - Probability Page/Excercise 15.1

Question 1

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

Solution 1

Number of times 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 girls        (iii)    No girl
Also, check whether the sum of these probabilities is 1.

Solution 2

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       Thus, the sum of all these probabilities is 1.                        Thus, the sum of all these probabilities is 1. 

Question 3

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.

Solution 3

Number of students born in August = 6
Total number of students = 40   = 

Question 4

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.

Solution 4

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:  

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
16000 or more	1	579	82	88

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.

Solution 5

Number of families surveyed = 2400   (i) Number of families earning Rs 10000 - 13000 per month and owning exactly 2 vehicles = 29
    Required probability =  (ii) Number of families earning Rs 16000 or more per month and owning exactly 1 vehicle = 579
     Required probability =  (iii) Number of families earning less than Rs 7000 per month and does not own any vehicle = 10       Required probability =  (iv)  Number of families earning Rs 13000 - 16000 per month and owning     more than 2 vehicles = 25
       Required probability =  (v)  Number of families owning not more than 1 vehicle = 10 + 160 + 0 + 305 + 1 + 535 + 2 + 469 + 1       + 579 = 2062       Required probability = 

Question 6

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.

Solution 6

Total number of students = 90   (i)  Number of students who obtained less than 20% marks in the test = 7
     Required probability = (ii)  Number of students who obtained marks 60 or above = 15 + 8 = 23
       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

Solution 7

Total number of students = 135 + 65 = 200   (i)  Number of students who like statistics = 135
     P(student likes statistics) =  (ii)  Number of students who do not like statistics = 65       P(student does not like statistics) = 

Question 8

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?

Solution 8

Total number of engineers = 40 
(i)  Number of engineers living at a distance of less than 7 km form their place of work = 9
     Required probability =  (ii)  Number of engineers living at a distance of more than or equal to 7 km from their place of work        = 40 - 9 = 31
      Required probability =  (iii)  Number of engineers living within a distance of   km from her place of work = 0
       Required probability = 0

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.

Solution 11

Total number of bags = 11
 Number of bags containing more then 5 kg of flour = 7
 Required probability =  

Question 12

A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The frequency distribution of the data obtained for 30 days is as follows:  

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

Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 -  0.16 on any of these days.

Solution 12

Number days for which the concentration of sulphur dioxide was in the interval of 0.12 - 0.16 = 2
Total number of days = 30
Required probability  =

Question 13

The blood groups of 30 students of class VIII are given in the following frequency distribution table:  

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

Use this table to determine the probability that a student of this class, selected at random, has blood group AB.

Solution 13

Number of students having blood group AB = 3
Total number of students = 30
Required probability =