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common fraction

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Sara tossed a fair coin five times, and Kaleb tossed a fair coin three times. There were five heads and three tails in the eight tosses. What is the probability that either Sara or Kaleb tossed exactly three heads? Express your answer as a common fraction.

  • common fraction -

    Probability that Sarah throws exactly 3 heads:

    Binomial[5,3] 2^(-5) = 10/32 = 5/16

    Probability that Sarah does not throw excatly 3 heads is:

    1 - 5/16 = 11/16

    Probability that Kaleb throws exactly 3 heads:

    1/8


    Probability that Kaleb does not throw excatly 3 heads is:

    1-1/8 = 7/8

    Probability that neither Kaleb nor Sarah throw exactly 3 heads is:

    11/16 * 7/8 = 77/128

    Probability that either Kaleb or Sarah throw exactly 3 heads is:

    1 - 77/128 = 51/128

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