Question

A king has 3 children. The first born is a son. What is the probability that the king has 3 sons

Answer 1

make a list of all possible outcomes, in order of age:

{GGG,GGB,GBG,BGG,GBB,BGB,BBG,BBB}.

As it is given that first one is a boy so we can rule out {GGG, GGB, GBG, GBB}

so the sample space reduce to {BGG, BGB, BBG, BBB}

so the probability that king has 3 sons =1 /4

or

another method

since the chance of a child being a son is 1/2, the chance of all three being sons is 1*(1/2)* (1/2) = 1/4

as the condition is given as first is a boy so the probability of first child to be son is 1