NCERT Solution: Probability
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
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.
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.
Number of students born in the month of August = 6
Total number of students = 40
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.
Number of times 2 heads come up = 72
Total number of times the coins were tossed = 200
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:
| 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 Rs10000 – 13000 per month and owning exactly 2 vehicles.
(ii) earning Rs16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than Rs7000 per month and does not own any vehicle.
(iv) earning Rs13000 – 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.
Total numbers of families = 2400
(i) Numbers of families earning Rs10000 –13000 per month and owning exactly 2 vehicles = 29
Required probability = 29/2400
(ii) Number of families earning Rs16000 or more per month and owning exactly 1 vehicle = 579
Required probability = 579/2400
(iii) Number of families earning less than Rs7000 per month and does not own any vehicle = 10 Required probability = 10/2400 = 1/240
(iv) Number of families earning Rs13000-16000 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
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.
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
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 | 135 |
| dislike | 65 |
Find the probability that a student chosen at random
(i) likes statistics, (ii) does not like it.
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
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 1 / 2 km from her place of work?
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
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