First slide

Theorems of probability

Question

A father has 3 children with at least one boy. The probability that he has 2 boys and 1 girl is

Moderate

A

1/4
B

1/3
C

2/3
D

None of these

Solution

Consider the following events:
A: Father has at least one boy.
B: Father has 2 boys and one girl
Then,
A = one boy and2 girls, 2 boys and one girl, 3 boys and no girl
$A \cap B$ = 2 boys and one girl
Now, the required probability is
$= P (A / B) = \frac{P (A \cap B)}{P (A)} = \frac{1}{3}$

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