Probability Ques 47
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: 47.(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
$\frac{\text{ All } 4 \text{ girls }}{(\text{ All } 4 \text{ girls } )+ (\text{ exactly } 3 \text{ girls } + 1 \text{ boy })+ (\text{ exactly } 2 \text{ girls } + 2 \text{ boys })}$
$=\frac{(\frac{1}{2}){ }^{4}}{(\frac{1}{2})^{4}+{ }^{4} C _3 (\frac{1}{2}){ }^{3} (\frac{1}{2})+{ }^{4} C _2 (\frac{1}{2})^{2} (\frac{1}{2})^{2}}=\frac{1}{1+4+6}=\frac{1}{11}$
BETA
