<s>[INST] 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? [/INST] 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%).</s>\ <s>[INST] explain that better so that I can understand how that works, break it down & give me step by step instructions on how it works? [/INST] 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.</s>