DISCUSS: Oldest Son A family with two children is randomly selected. Assume that the events of having a boy or a girl are equally likely. Find the following probabilities.

(a) The family has two boys given that the oldest child is a boy.

(b) The family has two boys given that one of the children is a boy.

(a)

To find:

The probability that the family has two boys given that the oldest child is a boy.

Given:

The family has two children. The events of having a girl (G) and boy (B) are equally likely.

The possible combinations will be BB, BG, GB, GG.

Approach:

Let S be the sample space and all outcomes are equally likely. The probability of an event E denoted by P(E) is,

P(E)=n(E)n(S)=number of favourable outcomes

(b)

To find:

The probability that the family has two boys given that one of the children is a boy.