Probability 3 Question 1
1. Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls; is
(2019 Main, 10 April I)
(a) $\frac{1}{17}$
(b) $\frac{1}{12}$
(c) $\frac{1}{10}$
(d) $\frac{1}{11}$
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Answer:
Correct Answer: 1. (d)
Solution:
- Let event $B$ is being boy while event $G$ being girl.
According to the question, $P(B)=P(G)=\frac{1}{2}$
Now, required conditional probability that all children are girls given that at least two are girls, is
All 4 girls
(All 4 girls $)+$ (exactly 3 girls +1 boy)
- (exactly 2 girls +2 boys)
$=\frac{\frac{1}{2}{ }^{4}}{\frac{1}{2}^{4}+{ }^{4} C _3 \frac{1^{3}}{}{ }^{3} \frac{1}{2}+{ }^{4} C _2 \frac{1}{2}^{2} \frac{1}{2}^{2}}=\frac{1}{1+4+6}=\frac{1}{11}$
