A family has 2 children. Find the probability that both are boys if it is known that

(i) at least one of the children is a boy

(ii) the elder child is a boy.

Given, A family has two children

To Find: Find the probability that both are boys

Explanation: Let us Assume Boy is B and Girl is G

So, The number of sample spaces are 4.

The sample space , S = {BB, BG, GB, GG}

Now, If Both are boys,

Then, Sample space, A = {BB}

The number of sample space, nA = 1

(i) at least one of the children is a boy

If there is at least one boy

B = {BB, BG, GB}

The number of sample space, nB = 3

P(B) =

Now,

The required probability P(A/B)

We know,

So,

Hence,

(ii) the elder child is a boy.

Let C = The elder child is a boy

So, The sample space , C_s = {BB, BG}

The number of sample space, nC = 2

Since

And,

Now, The required probability,

We know,

So,

Hence,