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
(a) Total number of families = 300
Let E be the event of selecting a family with one girl child.
Number of favourable outcomes = 165
P(E) = \frac{\mathrm{Number of favourable outcomes}}{\mathrm{Total number of outcomes}}
P(E) = \frac{165}{300}
P(E) = \frac{11}{20}
Hence, the probability of selecting a family with one girl child is \frac{11}{20}.
(b) Let A be the event of selecting a family with one or more girl child.
Number of favourable outcomes = 165 + 95 = 260
P(A) = \frac{260}{300}
P(A) = \frac{13}{15}
Hence, the probability of selecting a family with one or more girl child is \frac{13}{15}.
(c) Let B be the event of selecting a family with no boy child.
A family has no boy child when it has two girl children.
Number of favourable outcomes = 95
P(B) = \frac{95}{300}
P(B) = \frac{19}{60}
Hence, the probability of selecting a family with no boy child is \frac{19}{60}.
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