Question

Let the probability of the birth of twins of same gender being twice that of the twins of the different genders and the probability of two girls being twice of that of two boys, the probabilities of a Boy-Girl or Girl-Boy being equal. Given that the first born child is a boy, the probability that the other is also a boy, is

• A. $\frac{4}{7}$
• B. $\frac{8}{11}$
• C. $\frac{1}{2}$
• D. $\frac{5}{8}$

Answer 1

Answer: (A)

$P($ twins of different sex i.e. $BG$ or $GB)=\frac{1}{3}$ (BG or GB are mutually exclusive) and equally likely
$P($ twins of same sex ie. $BB$ or $GG)=\frac{2}{3}$
Let $P(GG)=2x\Rightarrow P(BB)=x$
$\therefore 3x=\frac{2}{3}\Rightarrow x=\frac{2}{9}$
$\therefore P(GG)=\frac{4}{9};P(BB)=\frac{2}{9}$
Also $P(BG)=\frac{1}{6};P(GB)=\frac{1}{6}$
$P(BB/BB\text{ or }BG)=\frac{P(BB)}{P(BB)+P(BG)}=\frac{\frac{2}{9}}{\frac{2}{9}+\frac{1}{6}}=\frac{4}{4+3}=\frac{4}{7}$