In his book ''PARADOX'' Professor Jim Al-Khalili poses the following question ( I have shortened it somewhat for brevity): You wish to buy two kittens. The pet shop has two sibling kittens, one black and one tabby. You ask if they are boy or girl and you have to consider two different responses from the pet shop owner.
a) She tells you: 'I have only checked one of them and it's a boy.'
b) She tells you: 'I have checked the tabby and it's a boy.'
The question to be answered is: What is the probability that they are both boys?
After giving some explanation, the professor concludes by writing: So you see the probobility that both kittens are boys changes from 1 in 3 to 1 in 2 as soon as you know which of the two cats has been discovered to be a boy.
My problem is that I can't grasp why the probability should change. After all, once you are told one of the kittens is a boy why should it matter to the probability of both being boys whether it is the black one or the tabby? Would someone care to explain where my understanding is wrong ?
P.S The professor also writes that this is the same situation as that in the Monty Hall Paradox. No doubt those who read this will be familiar with this old TV show conundrum.