Question

Consider a group of families each having 2 children. The two siblings of any given family can be of any combination of boy (b) and girl (g). What is the probability that a family has both children as boys given one child is boy? How does this compare to the probability of both children being boys? (Note: Drawing the Venn diagram of events and the sample space would make it quite easier to work with)

Please provide a venn diagram thanks

Answer 1

We have P(B)= 0.5 and P(G) = 0.5

A group of families each having 2 children, so the sample space contain 4 outcomes : { BB, BG, GB, GG }  

So P(BB) = 1/4 = 0.25 , P(BG) = 1/4 = 0.25 , P(GB) = 1/4 = 0.25 , P(GG) = 1/4 = 0.25 ,

Venn diagram :

Probability that a family has both children as boys given one child is boy :

P( B | B ) = P( BB ) / P(B) = 0.25 / 0.5 = 0.5  

P( B | B ) = 0.5

How does this compare to the probability of both children being boys?

The P(B|B) is the conditional probability we have found it using the conditional probability formula and P(BB) is the product of two independent events P(B)*P(B) = 0.5*0.5 = 0.25

So P(BB) = 0.25