1 Acey Deucey • Have a standard deck of 52 cards Ranks of cards: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A Three cards drawn (without replacement) What is probability that rank of third card drawn is between the ranks of the first two cards, exclusive? o E.g., if ranks of first two cards drawn are 4 and 9, then want probability that third card is a 5, 6, 7 or 8 • Solution set-up Let X = difference between rank of 1 st and 2 nd card P(X = 0) = 3/51 o After picking first card, there are 3 others with same rank o This is not really relevant. Just a warm-up to get you thinking! Acey Deucey Solution • Solution P(X = i ) = , where 1 i 12 o (13 – i ) ways to choose two ranks that differ by i o First card has 2/13 chance of being one of those 2 ranks o Second card is one of 4 cards (out of 51) that differ in rank by i Want: o Of remaining 50 cards, there are 4 cards of each ( i – 1) ranks 51 4 13 2 ) 13 ( i ) | first two between card rd 3 ( ) ( 12
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