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11 July, 23:29

During a single day at radio station WMZH, the probability that a particular song is played is 0.15. What is the probability that this song will be played on exactly 5 days out of 7 days? Round your answer to the nearest thousandth.

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  1. 11 July, 23:38
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    0.001

    Step-by-step explanation:

    This is a combination problem, so we need to calculate the combination of 7 choose 5, and then multiply by the probability of each event:

    Combination of 7 choose 5:

    C (7,5) = 7! / (5! * 2!) = 7*6/2 = 21

    This value means that we have 21 different possibilities of the 5 days we want being allocated in the 7 days

    Now, the probability of each event is:

    5 days playing the song: (0.15) ^5

    2 days not playing the song: (0.85) ^2

    So, the final probability is

    P = C (7,5) * (0.15) ^5 * (0.85) ^2 = 0.001
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