Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of kings.

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Solution

Let X denote the number of kings obtained in two draws. X takes the values 0, 1, 2. Let p denote the probability of getting king and q denote the probability of not getting the king.

therefore space space space straight p space equals space 4 over 52 equals space 1 over 13 comma space space space straight q space equals space 1 minus straight p space equals space 1 minus 1 over 13 space equals space 12 over 13 straight P left parenthesis straight X space equals space 0 right parenthesis space equals space straight q space straight q space equals space 12 over 13 cross times 12 over 13 space equals 144 over 169 straight P left parenthesis straight X space equals space 1 right parenthesis space equals space straight p space straight q space plus space straight q space straight p space equals space 1 over 13 plus 12 over 13 plus 12 over 13 cross times 1 over 13 space equals 12 over 169 plus 12 over 169 space equals 24 over 169 straight P left parenthesis straight X space equals space 2 right parenthesis space equals space straight p space straight p space equals space 1 over 13 cross times 1 over 13 space equals space 1 over 169

∴ probability distribution is

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Probability

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of kings.

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