Question

A pair has two children. If one of them is boy, then the probability that other is also a boy, is

• A. $\frac { 1 } { 2 }$
• B. $\frac { 1 } { 4 }$
• C. $\frac { 1 } { 3 }$
• D. None of these

Answer 1

Answer: (C)

$\frac { 1 } { 3 }$

Answer 2

Let $P ( A ) =$ probability of a boy in two children $= \frac { 3 } { 4 }$

Because cases are $B B , B G , G B , G G = 4$

Favourable cases are $B B , B G , G B = 3$

The probability that the second child is also boy is

$P ( A \cap B ) = \frac { 1 } { 4 }$

We have to find $P ( B / A ) = \frac { P ( A \cap B ) } { P ( A ) } = \frac { 1 / 4 } { 3 / 4 } = \frac { 1 } { 3 }$