From a group of 3 boys and 2 girls, two children are chosen at random, one after the other. If the first child chosen is a girl, then the probability that the second child chosen is a boy is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{3}{4}\)
Once a girl has been chosen first, 4 children are left: 3 boys and 1 girl. The second child is equally likely to be any of these 4, so the conditional probability is
\( \displaystyle P(\text{second boy}\,|\,\text{first girl}) = \frac{3}{4} \)
Why the other options are incorrect
Option (1) \(\displaystyle\frac{3}{5}\) — Incorrect. This is the chance of a boy from all 5 children; the girl already chosen is not available again.
Option (2) \(\displaystyle\frac{3}{10}\) — Incorrect. This is \(\frac{2}{5}\times\frac{3}{4}\), the probability that the first is a girl and the second a boy; here the first is already known to be a girl.
Option (4) \(\displaystyle\frac{1}{4}\) — Incorrect. This is the probability that the second child is the remaining girl.