Suppose that when a child is born, that there is a 50% chance it will be a girl

ID: 3304970 • Letter: S

Question

Suppose that when a child is born, that there is a 50% chance it will be a girl and a 50% chance it will be a boy.

1.What is the probability that a family with two children has two boys, given that it has at least one boy?

2.What is the probability that a family with two children has two girls, given that the first child is a girl?

Hint: These questions are subtly different. Carefully consider your sample space in each case.

Remember that your goal for these problems is not to arrive at the correct answer, but to

clearly and logically explain how to arrive at the correct answer.

P(G)=0.5 P(B)=0.5

In a family with 2 children there are four possibilities:

1) the first child is a boy and the second child is a boy BB

2) the first child is a boy and the second child is a girl BG

3) the first child is a girl and the second child is a boy GB

4) the first child is a girl and the second child is a girl GG

a) P(a family with two children has two boys, given that it has at least one boy)=1/3

b) P(a family with two children has two girls, given that the first child is a girl)=1/2

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