Question

A king has 2 children. What is the probability that both children are boys, given that a) the first child is a boy? b) at least one child is a boy?

Answer 1

Number of possible chances of two children are (Girl,Girl ), (Girl,Boy),(Boy,Girl) and (Boy,Boy)

i) The probability that first child is a boy is (i..e (Boy,Girl ) and (Boy, Boy) )

The probability that both children are boys and the first child is a boy is ( i.e. (Boy, Boy) )

The probability that both children are boys, given that the first child is a boy is

ii) The probability that at least one child is a boy is ( i.e.  (Girl,Boy),(Boy,Girl) and (Boy,Boy) )

The probability that both children are boys and at least one child is a boy is   ( i.e. (Boy, Boy) )

The probability that both children are boys, given that at least one child is a boy is