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A. Double Counting

# A. Double Counting - Handout A Double Counting Ref The...

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Handout A: Double Counting Ref: The Probability Tutoring Book , C. Ash, IEEE Press, NJ, 1993, pp. 16-19. I’ll find the probability of a poker hand with two pairs. If I regard a poker hand as a committee, then the total number of hands is 52 5 ! " # \$ % & . Now I need to get the number of favorable hands. To get started, it often helps to write out some favorable outcomes—the steps involved in constructing an outcome may suggest the slots to be filed in the counting process. Here are some poker hands with two pairs: Hand 1: Q H , Q D , J S , J H , A H Hand 2: 4 C ,4 H , K D , K C ,2 H First let’s analyze an incorrect method . Each outcome involves a first face (e.g., queen), two suits in that face (e.g., heart and diamond), a second fact (e.g. jack), two suits in that face (e.g., spade and heart), and a fifth card not of either face (to avoid a full house). So use these slots: Step 1: Pick a face value. Step 2: Pick 2 of the 4 cards in that face. Step 3: Pick another face value.

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