Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that
(i) the youngest is a girl?

(ii) atleast one is a girl?

Question

Philoid · Accepted Answer

Let B and G stands for boy and girl child respectively. Then the sample space if a family has two children will be,

S = {BB,BG,GB,GG}

Let A be the event when both children are girls.

A = {GG} ⇒

Conditional probability that both are girls if

(i) the youngest is a girl

Let B be the event when youngest child is a girl.

B = {BG,GG}

Now,

∵ A∩B={GG}

Thus, Conditional probability that both children are girls if the youngest is a girl is .

Conditional probability that both are girls if

(ii) atleast one is a girl

Let C be the event when atleast one child is a girl.

C = {BG,GB,GG}

Now,

∵ A∩C={GG}

Thus, Conditional probability that both children are girls if atleast one child is a girl is .

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that(i) the youngest is a girl?(ii) atleast one is a girl?