Question

It is given that a family of $3$ children has two girls, what is the probability that the other child is also a girl?

• A. $0.50$
• B. $0.75$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

Answer: (D)

$\frac{1}{4}$

Probability that child is girl=1/2

Probability that the other child is also a girl given that two are already girls=

$\frac{Probabiltythatchildisagirlgiventwoarealreadygirl}{Probabiltythatchildisgirl}$

=$\frac{{}^3{C}_1\ast 1/2\ast 1/2\ast 1/2}{{}^3{C}_1\ast 1/2}=1/4$