you choose 2 balls at random, one at a time. Are you more likely to chose 2 white balls in a row when you replace the first ball or when you don't replace the first ball? Explain.

Answer 1

Think about it. Let's say I have 8 balls and two are white The first time I have a 2/8 or 1/4 chance of choosing a white ball. If I replace it, I again have a 1/4 chance.

(1/4)(1/4) = 1/16

But, if I don't replace it, I now have a 1/7 chance the 2nd time.

(1/4)(1/7) = 1/28

Well, 1/16 is way bigger than 1/28, so you have a better chance with replacement.

Answer 2

Let's suppose there are N balls of which P are white.

With replacement the probability is (P/N)².

Without replacement the probability is P(P-1)/[N(N-1}

You can see that the answer depends on the how many white balls there are and how many balls there are in total.