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24 December, 12:00

Suppose that a high school marching band has 86 members. Of these 86 band members, 26 are seniors, 17 play the trumpet, and 4 are seniors who play the trumpet. What is the probability that a randomly selected band member is a senior given that he or she plays the trumpet

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  1. 24 December, 12:30
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    Answer: 0.3023

    Step-by-step explanation:

    86 band members

    26 are senior, 17 plays trumpet. If 4 are seniors and play trumpet, we solve this using the bayes theorem of conditional probability.

    Probability of choosing band member that plays trumpet = 17/86 = 2/43.

    Probability of choosing a senior that plays trumpet = 4/26

    Probability that a chosen member is a senior given that he plays trumpet = (2/43) / (4/26)

    = 0.3023.
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