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29 August, 18:49

The deck of a card game is made up of 108 cards. Twenty-five each are red, yellow, blue, and green, and eight are wild cards. Each player is randomly dealt a seven-card hand. What is the probability that a hand will contain exactly two wild cards? What is the setup for this problem (that you would type into your calculator) ? (Do not actually find the probability.)

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  1. 29 August, 19:08
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    Given Information:

    Total cards = 108

    Red cards = 25

    yellow cards = 25

    Blue cards = 25

    Green cards = 25

    Wild cards = 8

    Required Information:

    Probability that a hand will contain exactly two wild cards in a seven-hand game = ?

    Answer:

    P = (₈C₂*₁₀₀C₅) / ₁₀₈C₇

    Step-by-step explanation:

    The required probability is given by

    P = number of ways of interest/total number of ways

    The total number of ways of dealing a seven-card hand is

    ₁₀₈C₇

    We want to select exactly 2 wild cards and the total wild cards are 8 so the number of ways of this selection is

    ₈C₂

    Since the game is seven-card hand, we have to get the number of ways to select remaining 5 cards out of (108 - 8 = 100) cards.

    ₁₀₀C₅

    Therefore, the setup for this problem becomes

    P = number of ways of interest/total number of ways

    P = (₈C₂*₁₀₀C₅) / ₁₀₈C₇

    This is the required setup that we can type into our calculators to get the probability of exactly two wild cards in a seven-hand card game with 8 wild cards and 108 total cards.
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