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Math Help - Basic Probability

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    Basic Probability

    A sample of 5 accounts is chosen without replacement from a set of 20. From past experience it is known that 20% of the accounts are in error. What is the probability that not more than two errors will occur in the sample?
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  2. #2
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    Hello, matty888!

    A sample of 5 accounts is chosen without replacement from a set of 20.
    From past experience it is known that 20% of the accounts are in error.
    What is the probability that not more than two errors will occur in the sample?

    There are 20 accounts: . \begin{array}{cc}\text{16 are good (G)} \\ \text{4 have errors (E)} \end{array}

    There are: . {20\choose5} \:=\:15,504 possible samples.

    We want the probability that there are:
    . . 0 errors or 1 error or 2 errors.


    0 E and 5 G: . {4\choose0}{16\choose5} \:=\:4368 ways.

    1 E and 4 G: . {4\choose1}{16\choose4} \:=\:1820 ways.

    2 E and 3 G: . {4\choose2}{16\choose3} \:=\:3360 ways.

    Hence, there are: . 4368 + 1820 + 3360 \:=\:9548 ways to get 0, 1 or 2 Errors.


    Therefore: . P(\text{0, 1 or 2 E}) \;=\;\frac{9548}{15,504} \;=\;\boxed{\frac{2387}{3876}}

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