Two cards are drawn from the pack of 52 cards. Find the probability that both are diamonds or both are kings.

Question

Two cards are drawn from the pack of 52 cards. Find the probability that both are diamonds or both are kings.

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Thanh Hà 5 years 2021-08-07T12:11:39+00:00 1 Answers 1018 views 1

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  1. Thunguyet
    0
    2021-08-07T12:12:54+00:00
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    Answer as a fraction = 14/221 (exact)

    Answer in decimal form = 0.0633 (approximate)

    Answer in percent form = 6.33% (approximate)

    =========================================================

    Work Shown:

    There are 13 diamond cards. The probability of getting a diamond card is 13/52 = 1/4.

    Assuming the first card is not replaced, the probability of getting another diamond card is 12/51. Note how I subtracted 1 from the numerator and denominator of 13/52 to get 12/51.

    Multiply the two fractions to get

    (1/4)*(12/51) = 12/204 = 1/17

    The probability of getting two diamonds in a row is 1/17

    We’ll use this later, so let A = 1/17.

    ———————

    There are 4 kings. The probability of pulling out a king is 4/52 = 1/13

    The probability of pulling out another king is 3/51 = 1/17

    The probability of pulling out two kings in a row is (1/13)*(1/17) = 1/221

    Let B = 1/221

    ———————

    Add the values of A and B

    A+B = 1/17 + 1/221

    A+B = 13/221 + 1/221

    A+B = (13+1)/221

    A+B = 14/221

    A+B = 0.0633 which is approximate

    That converts to 6.33% when you move the decimal point over 2 spots to the right.

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