Probability Question 170
A pair has two children. If one of them is a boy, then the probability that the other is also a boy, is
Options:
A) $ \frac{1}{2} $
B) $ \frac{1}{4} $
C) $ \frac{1}{3} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ P(A)= $ probability of two boys in two children $ =\frac{1}{4} $
Because cases are $ BB,BG,GB,GG $ with 4 possibilities
Favourable cases are $ BB, BG, GB = 3 $
The probability that the second child is also a 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}. $
BETA
