A survey was conducted on 300 families having 2 children each. The results obtained are given below.
| Number of girl child | Number of families |
|---|---|
| 2 | 95 |
| 1 | 165 |
| 0 | 40 |
| Total | 300 |
If one family is selected at random, find the probability that it will have:
(a) one girl child
(b) one or more girl child
(c) no boy child
Show SolutionHide Solution↓
(a) Total number of families = 300
Let E be the event of selecting family with one girl child,
∴ Number of favorable outcomes = 165
P(E) = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{165}{300} = \frac{11}{20}.$
Hence, probability of selecting family with one girl child = $\frac{11}{20}.$
(b) Let A be the event of selecting family with one or more girl child,
∴ Number of favorable outcomes = 165 + 95 = 260
P(A) = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{260}{300} = \frac{13}{15}.$
Hence, probability of selecting family with one or more girl child = $\frac{13}{15}.$
(c) Let B be the event of selecting family with no boy child.
A family will have no boy child, if there are 2 girl child in the family.
∴ Number of favorable outcomes = 95
P(B) = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{95}{300} = \frac{19}{60}.$
Hence, probability of selecting family with no boy child = $\frac{19}{60}.$