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For this question, assume I have a standard deck of cards (52 cards, 13 of each set). My question is: if I were to randomly draw 7 cards, how would I calculate the probability of at least one of those cards being a Spade? Then, supposing no spades were drawn, how do I calculate the probability that the next card I draw is a spade? |
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For problem 1, it is easier to work out the probability that none are spades. This is $1 - 39/52 * 39/51 * 39/50 .... * 39/46) = .204$ the probability of at least 1 spade is 1 - the above, or about .8. If you have drawn 7 cards and no spades, then there are 45 cards in the deck and 13 are spades, so the chance that the next is a spade is 13/45 |
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