A father has three children with at least one boy. The probability that he

Question

A father has three children with at least one boy. The probability that he has two boys and one girl is

Options:

A . 14

B . 37

C . 13

D . 25

Answer: Option B
:
B
Let A be the event that father has at least one boy and B be the event that he has 2boys and one girl.

P (A) = P (1 b o y, 2 g i r l) + P (2 b o y, 1 g i r l) + P (3 b o y, n o g i r l) = \frac{3 C_{1} + 3 C_{2} + 3 C_{3}}{2^{3}} = \frac{7}{8}

P (A ⋂ B) = P (2 b o y, 1 g i r l) = \frac{3}{8}

H e n c e P (\frac{B}{A}) = \frac{P (A ⋂ B)}{P (A)} = \frac{3}{7} .

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