I have this question: A person has three children with at least one boy. Find the probability of having at least two boys among the children.
My intuition about the problem is this-- the person has at least one boy means total possible outcome can be :
it cannot have GGG, so for at least two boy we have BBB,BBG,BGB,GBB as favorable outcome this gives us probability 4/7.
but the solution given in book goes as --->
Event = having at least two boy
The event is occurring under the following situations:
- second is a boy and third is a girl OR
- second is a girl and third is a boy OR
- second is a boy and third is a boy
so the probability will be
(1/2) *(1/2) + (1/2) *(1/2) + (1/2) *(1/2) = 3/4
So please tell me is my intuition is correct or the solution given in the book