Question

A family has two children. What is the probability that both the children are boys given that at least one of them is a boy?

Answer 1

To find P (both children are males, if it is known that at least one of the children is male).

A: Event that both children are male, and B: event that at least one of them is a male.

A: {MM} and B: {MF, FM, MM} →→ P (A ∩∩ B) = {MM}

Probability that both are males, if we know one is a female =P(A/B)=P(A∩B)/P(B)

(P(A∩B)P(B))

Given S = {MM, MF, FM, FF}, we can see that: P (A) = 1414; P (B) = 3434; P (A ∩∩ B) = 1414

Therefore P(B/A)=P(A∩B)/P(A) =(1/4)/(3/4)=1/3