Answer:
Answer = 1/2
Step-by-step 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
