Question

A mathematician has two kids. the older one is a boy. what is the probability that they are both boys?

Answer 1

In a family with 2 children there are four possibilities:

1) the first child is a boy and the second child is a boy (bb)

2) the first child is a boy and the second child is a girl (bg)

3) the first child is a girl and the second child is a boy (gb)

4) the first child is a girl and the second child is a girl (gg)

Since we are given that older one is boy there are two possibilities: bg or bb Out of those two possibilities the only one with two boys is bb. Hence the probability is 1/2


@skb

Answer 2

The answer is actually 1/3

• Let's take a look at this there .
• Actually in a two kids family there is 4 types of combined probability.
• Boy and a boy / sister and sister / Big brother and younger brother/ younger brother and big sister.
• Since we know once of them is a boy we should move the two sisters out
• Meaning that probability of the second kid being a boy is 1/3.
• This is actually a famous paradox called boy or girl paradox written by Martin Garden.