Question

A couple has two children. Find the probability that both children are males, if it is known that at least one of the children is male.

Answer 1

If a couple has two children then the sample space is

S = { (b, b),(b, g),(g, b),(g, g)}

Let E and F respectively denote the events that both children are males and at least one of the children is a male.

∴ E ∩ F = {(b, b)} ⇒ P(E ∩ F) = 1/4

P (E) = 1/4; P (F) = 3/4

⇒ P(E/F) = P(E∩F)/P(F) = 4/3 / 4 = 1/3