Ex - 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
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:
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
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 = 24Question 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.
(i) 2 girls (ii) 1 girls (iii) No girl
Also, check whether the sum of these probabilities is 1.
Solution
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
Number of students born in August = 6
Total number of students = 40
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
Number of times 2 heads come up = 72
Total number of times the coins were tossed = 200
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.
(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
Number of families surveyed = 2400
(i) Number of families earning Rs 10000 - 13000 per month and owning exactly 2 vehicles = 29
Required probability =
Required probability =
(ii) Number of families earning Rs 16000 or more per month and owning exactly 1 vehicle = 579
Required probability =
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 =
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.
(ii) Find the probability that a student obtained marks 60 or above.
Solution
Total number of students = 90
(i) Number of students who obtained less than 20% marks in the test = 7
Required probability =
Required probability =
(ii) Number of students who obtained marks 60 or above = 15 + 8 = 23
Required probability =
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
(i) likes statistics, (ii) does not like it
Solution
Total number of students = 135 + 65 = 200
(i) Number of students who like statistics = 135
P(student likes statistics) =
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?
(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
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 =
(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 =
Required probability =
(iii) Number of engineers living within a distance of km from her place of work = 0
Required probability = 0
km from her place of work = 0Required 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
Total number of bags = 11
Number of bags containing more then 5 kg of flour = 7
Required probability =
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
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 =
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
Number of students having blood group AB = 3
Total number of students = 30
Required probability =
Total number of students = 30
Required probability =
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