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Math Help - Probability question, please help

  1. #1
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    Probability question, please help

    Please show all work to receive full credit.

    1. Jeff owns 1 red shirt, 4 blue shirts, 5 white shirts, and 3 black shirts. He randomly selects four shirts to pack for vacation.

    a) What is the probability he packs all white shirts?
    b) What is the probability he packs the red shirt?
    c) What is the probability he packs at least one blue shirt?


    2. For the month of January in Cincinnati, 83.9% of the days are 32 F or below. Also in the month of January in Cincinnati, 23.2% of the days are 32 F or below and snowy. What is the probability a randomly selected day in January in Cincinnati will be snowy if it is 32 F or below?


    I'm racking my brain on these, for some reason probability questions just are clicking for me.

    I think the second one is setup .232/.869=.266
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Probability question, please help

    1.)

    How many ways can Jeff choose 4 shirts from a total of 13 shirts?

    a) How many ways can Jeff choose 4 white shirts from 5 white shirts?

    b) Given that Jeff has chosen a red shirt, how many ways are there for him to pick 3 shirts from the remaining 12?

    c) We know it is certain that he will pack 0, 1, 2, 3, or 4 blue shirts. Let X be the event that he packs 0 blue shirts and Y be the event that he packs 1, 2, 3, or 4 blues shirts. So we know:

    P(X)+P(Y)=1

    P(Y)=1-P(X)

    So now we need only compute the probability that he packs no blue shirts to answer the question.

    So, how many ways are there to pick 4 shirts from the remaining 9 shirts?
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