This is a problem of conditional probability:

There are two boxes X and Y. X contains 5 balls: 2 are blue, 2 white and 1 is gray. Y contains 4 balls: 2 are blue, 1 is white and 1 is gray.

I have to calculate the probability of both balls being white given that both are of the same colour. One ball is going to be taken from each box.

This problem, at least when I look to the formula of conditional probability **((P(A|B) = P(A and B) / P(B))**, isn't very intuitive to me.

In this case, shouldn't the probability be **P(White and White | Same Colour) = P[(White and White) and Same Colour)/P(Same Colour)**?

My text book says it's going to be **P(White and White) / P(Same Colour)**.

Could you guys help? Thank you very much and sorry about the wall text.

Edit: missed a sentence.