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Math Help - Impurities probability problem

  1. #1
    VoV
    VoV is offline
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    Impurities probability problem

    Hi guys! I'm new in theory of probability and I'm having a hard time solving a probability problem. I'll be really grateful if you explain to me the solution.
    So here's the problem:

    Test for impurities commonly found in drinking water from private wells showed that 30% of all wells in a particular country have impurity A. If a random sample of five wells is selected from the large number of wells in the country, what is the probability that:

    a) Exactly three will have impurity A?
    b) At least three?
    c) Fewer than three?
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  2. #2
    MHF Contributor
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    For a)

    There are \binom{5}{3} ways to select exactly 3 wells from the sample of 5.

    Therefore the probability is \binom{5}{3}0.3^30.7^2

    For b)

    At least 3 means 3, 4 or 5...

    The probability of 4 having impurity A is \binom{5}{4}0.3^40.7

    The probability of 5 having A is 0.3^5

    The sum of these 2 probabities and the answer to a) is the answer to b)

    For c), just find the probability of 0, 1 or 2 having A, or subtract the answer for b) from 1
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