NCERT Solutions Class 9 Mathematics Chapter 15 Probability

Exercise 15.1

Q.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.
Sol.1) Let 𝐸 be the event of hitting the boundary
Then 𝑃(𝐸) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑖𝑚𝑒𝑠 𝑏𝑎𝑡𝑤𝑜𝑚𝑎𝑛 ℎ𝑖𝑡𝑠 𝑡ℎ𝑒 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦/𝑇𝑜𝑡𝑎𝑙 𝑛𝑜.𝑜𝑓 𝑏𝑎𝑙𝑙𝑠 𝑠ℎ𝑒 𝑝𝑙𝑎𝑦𝑠 
= 6/30 = 1/5 = 0.2
∴ probability of not hitting the boundary = 1 −probablity of hitting the boundary
= 1 − 0.2 = 0.8

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

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.
Sol.2) Total numbers of families = 1500
(i) Numbers of families having 2 girls = 475
Probability = Numbers of families having 2 girls/Total numbers of families
= 475/1500
= 19/60
(ii) Numbers of families having 1 girls = 814
Probability = Numbers of families having 1 girls/Total numbers of families
= 814/1500
= 407/750
(iii) Numbers of families having 2 girls = 211
Probability = Numbers of families having 0 girls/Total numbers of families
= 211/1500
Sum of the probability = 19/60 + 407/750 + 211/1500 
= 475 + 814 + 211/1500 = 1500/1500 = 1
Yes, the sum of these probabilities is 1.

Q.3) Refer to Example 5, Section 14.4, Chapter 14. Find the probability that a student of the class was born in August.

Sol.3) Total numbers of students = 40
Numbers of students = 6
Required probability = 6/40 = 3/20

Q.4) 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.
Sol.4) Number of times 2 heads come up = 72
Total number of times the coins were tossed = 200
Required probability = 72/200 = 9/25

Q.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.
Sol.5) Total numbers of families = 2400
(i) Numbers of families earning 𝑅𝑠. 10000 – 13000 per month and owning exactly 2 vehicles = 29
Required probability = 29/2400
(ii) Number of families earning Rs.16000 or more per month and owning exactly 1 vehicle = 579
Required probability = 579/2400
(iii) Number of families earning less than Rs.7000 per month and does not own any vehicle = 10
Required probability = 10/2400 = 1/240
(iv) Number of families earning Rs.13000-16000 per month and owning more than 2 vehicles = 25
Required probability = 25/2400 = 1/96
(v) Number of families owning not more than 1 vehicle = 10 + 160 + 0 + 305 + 1 + 535 +
2 + 469 + 1 + 579 = 2062
Required probability = 2062/2400 = 1031/1200

Q.6) Following table shows the performance of two sections of students in mathematics test of 100 marks.

(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.
Sol.6) Total numbers of students = 90
(i) Numbers of students obtained less than 20% in the mathematics test = 7
Required probability = 7/90
(ii) Numbers of student obtained marks 60 or above = 15 + 8 = 23
Required probability = 23/90

Q.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.

Find the probability that a student chosen at random
(i) likes statistics, (ii) does not like it.
Sol.7) Total numbers of students = 135 + 65 = 200
(i) Numbers of students who like statistics = 135
Required probability = 135/200 = 27/40
(ii) Numbers of students who does not like statistics = 65
Required probability = 65/200 = 13/40

Q.8) The distance (in km) of 40 engineers from their residence to their place of work were found as follows :
  5        3      10       2        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 1/2 km from her place of work?
Sol.8) Total numbers of engineers = 40
(i) Numbers of engineers living less than 7 km from her place of work = 9
Required probability = 9/40
(ii) Numbers of engineers living less than 7 km from her place of work = 40 – 9 = 31
Required probability = 31/40
(iii) Numbers of engineers living less than 7 km from her place of work = 0
Required probability = 0/40 = 0

Q.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.
Sol.11) Total no. of bags examined = 11
P (a bag weighing more than 5 kg) = No. of bags which weigh more than 5 kg/Total no. of bags
= 7/11

Q.12) A study was conducted to find out the concentration of sulphur dioxide in the air parts per million (ppm) of a certain city. The data obtained for 30 days is as follows :
0.03   0.08   0.08   0.09   0.04   0.17
0.16   0.05   0.02   0.06   0.18   0.20
0.11   0.08   0.12   0.13   0.22   0.07
0.08   0.01   0.10   0.06   0.09   0.18
0.11   0.07   0.05   0.07   0.01   0.04
Using this table, find the probability of the concentration of sulphur dioxide in the interval
0.12-0.16 on any of these days.
Sol.12) Total numbers of days data recorded = 30 days
Numbers of days in which sulphur dioxide in the interval 0.12 − 0.16 = 2
Required probability = 2/30 = 1/15

Q.13) The blood groups of 30 students of class VIII are recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O
Use this table to determine the probability that a student of this class, selected at random, has blood group AB.
Sol.13) Total numbers of students = 30
Numbers of students having blood group AB = 3
Required probability = 3/30 = 1/10