Suppose we are playing draw poker. We are dealt 5 cards from a well-shuffled deck, which contains four spades and another card of a different suit. We decide to discard the card of a different suit and draw one card from the remaining cards to complete a flush in spades. Determine the probability of completing the flush.
closed as off-topic by TheGeekGreek, Leucippus, Sahiba Arora, Namaste, Siong Thye Goh Jul 20 '17 at 0:59
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The deck starts with 52 cards and 13 of each suit. Once the 5 cards are dealt, 47 cards remain in the deck, 9 of them being spades and 38 being the other three suits. The probability of completing the flush is the probability of pulling a spade from the remaining 47 cards. Therefore, the probability is 9/47.
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