JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Probability

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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:

(A) $\frac{1}{10}$
(B) $\frac{1}{17}$
(C) $\frac{1}{12}$
(D) $\frac{1}{11}$ ✓ Correct

Answer: (D)

Solution

Each child is equally likely a boy or girl, and there are four children in all. We want the chance that all four are girls given that at least two are girls; since all four girls lies inside at least two girls, this is

\frac{P ( all four girls )}{P ( at least two girls )}

. Here

P (all four) = (\frac{1}{2})^{4} = \frac{1}{16}

, and

P (at least two) = \frac{( 2 4 ) + ( 3 4 ) + ( 4 4 )}{16} = \frac{6 + 4 + 1}{16} = \frac{11}{16}

. The ratio is

\frac{1/16}{11/16} = \frac{1}{11}

JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Single correct option

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JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Probability

Solution

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