Alice has a bowl with 8 balls. Three of the balls are white and the rest are black. Bob picks two balls from the bowl at random. What is the probability that both balls are white?
user
If Bob picks the balls with replacement, the probability is 9/64 which is approximately 14%. Without replacement, the probability is 3/28 (approximately 10%).
assistant
explain that better so that I can understand how that works, break it down & give me step by step instructions on how it works?
user
If Bob picks the balls with replacement the chance of getting a white ball is 3 (the number of white balls) out of 8 (the total number of balls), i.e. 3/8 or 37.5%. If it is 'and and' (both the first AND the second ball should be white) you need to use the multiplication rule. So 3/8 * 3/8 = 9/64.

If you do not use replacement the first is still 3/8 like above. But the second ball is 2/7 since there is only 2 white balls left and only 7 left in total. Again you need to multiply. So now its 6 / 56 which can be reduced to 3 / 28.
assistant