Question

Suppose a family has three children.find the probability that the first two children born are boys. What is the probability that the last two children are girls?

Answer 1

`1/4 and 1/4`

Explanation:

There are 2 ways to work this out.

Method 1. If a family has 3 children, then the total number of different boy-girl combinations is 2 x 2 x 2 = 8

Of these, two start with (boy, boy ...) The 3rd child can be a boy or a girl, but it does not matter which.
So, `P(B, B) = 2/8 = 1/4`

Method 2 . We can work out the probability of 2 children being boys as : `P(B, B) = P(B) xx P(B) = 1/2 xx 1/2 = 1/4`

In exactly the same way, the probability of the last two children both being girls can be:
(B, G, G) or (G, G, G) `rArr` 2 of the 8 possibilities. So, `1/4`

OR: `P(? , G, G) = 1 xx 1/2 xx 1/2 = 1/4`

(Note: The probability of a boy or a girl is 1)