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.
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.
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