Exercise 15.1
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.
Answer
Total numbers of balls = 30
Numbers of boundary = 6
Numbers of time she didn't hit boundary = 30  6 = 24
Probability she did not hit a boundary = 24/30 = 4/5
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.
Answer
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.
3. Refer to Example 5, Section 14.4, Chapter 14. Find the probability that a student of the class was born in August.
Answer
Total numbers of students = 40
Numbers of students = 6
Required probability = 6/40 = 3/20
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.
Answer
Number of times 2 heads come up = 72
Total number of times the coins were tossed = 200
Required probability = 72/200 = 9/25
5. An organisation 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 ₹10000 – 13000 per month and owning exactly 2 vehicles.
(ii) earning ₹16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than ₹7000 per month and does not own any vehicle.
(iv) earning ₹13000 – 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.
Answer
Total numbers of families = 2400
(i) Numbers of families earning ₹10000 –13000 per month and owning exactly 2 vehicles = 29
Required probability = 29/2400
(ii) Number of families earning ₹16000 or more per month and owning exactly 1 vehicle = 579
Required probability = 579/2400
(iii) Number of families earning less than ₹7000 per month and does not own any vehicle = 10 Required probability = 10/2400 = 1/240
(iv) Number of families earning ₹1300016000 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
6. Refer to Table 14.7, Chapter 14.
(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
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
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.
Answer
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
8. Refer to Q.2, Exercise 14.2. 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?
Answer
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 , 3 , 2 , 17 , 16 , 2 , 7 , 9 , 7 , 8 , 3 , 5 , 12 , 15 , 18 , 3 , 12 , 14 , 2 , 9 , 6 , 15 , 15 , 7 , 6 , 12
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
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.
Answer
Total numbers of bags = 11
Numbers of bags containing more than 5 kg of flour = 7
Required probability = 7/11
12.
In Q.5, Exercise 14.2, you were asked to prepare a frequency distribution table, regarding 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 0.120.16 on any of these days.
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
Answer
Total numbers of days data recorded = 30 days
Numbers of days in which sulphur dioxide in the interval 0.120.16 = 2
Required probability = 2/30 = 1/15
13. In Q.1, Exercise 14.2, you were asked to prepare a frequency distribution table regarding 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.
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.
Answer
Total numbers of students = 30
Numbers of students having blood group AB = 3
Required probability = 3/30 = 1/10
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