A family has two children. The probability that both the children are boys, given that at least one of them is a boy, is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{1}{3}\)
With B for boy and G for girl (elder child first), the four equally likely cases are BB, BG, GB, GG.
Let E = both are boys = {BB} and F = at least one is a boy = {BB, BG, GB}. Then \(E \cap F = \{BB\}\).
By the conditional probability formula:
\( \displaystyle P(E \mid F) = \frac{P(E \cap F)}{P(F)} \)
\( \displaystyle = \frac{1/4}{3/4} \)
\( \displaystyle = \frac{1}{3} \)
NCERT (2026-27 edition):
Conditional Probability
