A couple has 2 children, the probability that both are girls given that the youngest is a girl is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1/2
Write each outcome as (elder, younger): the sample space is {BB, BG, GB, GG}, all equally likely.
Let E = both are girls = {GG} and F = the youngest is a girl = {BG, GG}. Then E ∩ F = {GG}.
\( \displaystyle P(E|F)=\frac{P(E\cap F)}{P(F)}=\frac{1/4}{2/4} \)
\( \displaystyle =\frac{1}{2} \)
Why the other options are incorrect
Option (2) 1/4 — Incorrect. \( \frac{1}{4} \) is P(both girls) with no condition; the condition cuts the sample space down to BG and GG.
Option (3) 3/4 — Incorrect. \( \frac{3}{4} \) is the probability of at least one girl, a different event.
Option (4) 1 — Incorrect. The event F also contains BG, where the elder child is a boy, so the probability is less than 1.
NCERT (2026-27 edition):
Conditional Probability
