A couple has 2 children. Find the probability that both are boys, if it is known that (i) one of them is a boy (ii) the older child is a boy.

Sample space = [{GG}, {BB},{GB},{BG}]

(i)

Given, one of two children are boy

So, for both to be boys, the other one should also be boy.

A = one of them is boy [{BG}, {GB}, {BB}]

B = Both are boys {BB}

Now A∩ B = {BB}

P(A) = 3/4

P(B)=1/4

P (A∩ B) = 1/4

Therefore,

We know when we have to find the probability of event B given that A has occurred, the formula is:

(ii)

Given, older child is a boy,

for both of them to be boys, the younger one should also be boy.

A = older child is boy [{BG}, {BB}]

B = Both are boys {BB}

Now A∩ B = {BB}

P(A) = 2/4

P(B)=1/4

P (A∩ B) = 1/4

Therefore,

We know when we have to find the probability of event B given that A has occurred, the formula is: