Question

Your neighbor has 2 children. He picks one of them at random and comes by your house; he brings a boy named Joe (his son).

What is the probability that Joe’s sibling is a brother?

Answer 1

Answer = 1/2

Explanation:

Consider the experiment of selecting a family with two children

The sample space for the family = 4

The possible outcome for the two children = {BB, BG, GB, GG}

where B = boy

G = girl

Let X be the event that your neighbor has a son.

Let Y be the event that your neighbor randomly chose one of his two children and chose a son.

Pr(Y|X) = Pr(YnX) / Pr(Y)

= Pr({BB}) / [Pr(Y|{BB})P({BB}) + P(Y|{BG})P({BG}) + P(Y|{GB})P({GB}) + P(Y

|{GG})P({GG}]

= 1/4 / [1(1/4) + (1/2)(1/4) + (1/2)(1/4) + 0(1/4)]

= 1/4/ 1/2

= 1/2