5lb Chips Probability Q

GRE Quant Problem Solving
1

Hello all, this question is from the 5lb book:

A bag contains 6 black chips numbered 1–6 respectively and 6 white chips numbered 1–6 respectively. If Pavel reaches into the bag of 12 chips and removes 2 chips, one after the other, without replacing them, what is the probability that he will pick black chip #3 and then white chip #3?

So my confusion is - Greg seems to really emphasize in PrepSwift that the order of the chips or marbles or whatever pulled from the bag doesn’t change its probability of being pulled in any order, even without replacement. So my thought process is that the black chip has a 1/12 change of being pulled no matter the order, and the same goes for the white chip. So even though the white chip is pulled second, I still listed its probability as 1/12, meaning the final probability is (1/12)^2 = 1/144. But this is the incorrect approach - instead, we are supposed to select the white chip’s probability as 1/11 because we are doing this without replacement.

Can somebody help clarify where I am applying the concepts from PrepSwift incorrectly? Thanks!

2

Initially, when all the chips are in the bag, the probability of pulling each would be 1/12.
But once one chip is already removed, without replacing them, the total number of chips in the bag remaining are only 11.
Hence, then the probability of all the remaining 11 chips would now become 1/11.

3

So connecting it to the Gregmat problems where they are asking about the probability of pulling a green marble out fifth, is that essentially the only time of non-replacement problems where we don’t change the denominator?