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Math Help - Probability

  1. #1
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    Probability

    A box of 50 fuses contains five which are defective. If I take a sample of 20 out of the box, calculate the probability of there being at least two defective fuses.

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  2. #2
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    Hello, BabyMilo!

    A box of 50 fuses contains five which are defective.
    If I take a sample of 20 out of the box, calculate the probability
    of there being at least two defective fuses.

    There are: . _{50}C_5 \:=\:{50\choose5} possible sampes.


    We have: . \begin{array}{c}\text{5 bad} \\ \text{45 good} \end{array}


    The opposite of "at least 2 bad" is "0 bad or 1 bad".


    0 bad, 20 good: . P(\text{0 bad}) \;=\;\frac{{5\choose0}{45\choose20}} {{50\choose20}}

    1 bad, 19 good: . P(\text{1 bad}) \;=\;\frac{ {5\choose1}{45\choose19}} {{50\choose20}}


    . . Hence: . P(\text{0 or 1 bad}) \;=\;\frac{{5\choose0}{45\choose20}} {{50\choose20}} + \frac{ {5\choose1}{45\choose19}} {{50\choose20}}


    Therefore: . P(\text{at least 2 bad}) \;=\;1 - \left[\frac{{5\choose0}{45\choose20}} {{50\choose20}} + \frac{ {5\choose1}{45\choose19}} {{50\choose20}}\right]



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  3. #3
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    Perfect.
    Thanks.
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