There are 5 white and 8 black socks in a box. How many socks do you have to pick without looking and be certain that you will get:
1) two of the same colour?
2) two socks of each colour?
1) two of the same colour?
2) two socks of each colour?
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There are only 2 different colors, so you can pick one black, then one white, but then the next one will have to be either black or white, so the answer to 1) is 3 picks.
The worst you could do here, is pick 8 black socks (you will have at least one pair of black socks but no white socks). After you pick the 8 black socks, you will then HAVE to pick two white socks next, so the answer to 2) is 10 picks.
The worst you could do here, is pick 8 black socks (you will have at least one pair of black socks but no white socks). After you pick the 8 black socks, you will then HAVE to pick two white socks next, so the answer to 2) is 10 picks.
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1 There are three possible outcomes. On your first two selections either you pick two white or you pick two black or you pick one white and one black. Suppose that the first two socks you choose happen to different colours. How many socks do you have to pick in order to match one or the other of them? The question did not ask that you pick 2 white or 2 black but only that you have two matching in some colour.
2 Now, suppose that the first sock you pick is black and that the next 7 you pick are also black. How many do you have to pick before you have two that are white? This is a worst case example.
2 Now, suppose that the first sock you pick is black and that the next 7 you pick are also black. How many do you have to pick before you have two that are white? This is a worst case example.