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Math Help - failure time

  1. #1
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    failure time

    If the probability is 0.001 that a light bulb will fail on any given day,
    what is the probability that it will last at least 30 days?
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  2. #2
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    there are no new concepts from the other thread you posted.

    Can you see that the probability of it surviving 2 days is
    0.999 * 0.999

    And for 3 days its
    0.999 * 0. 999 * 0.999


    Can you generalise this to 30 days?
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  3. #3
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    Quote Originally Posted by ilikec View Post
    If the probability is 0.001 that a light bulb will fail on any given day,
    what is the probability that it will last at least 30 days?
    Pr(at least 30 days) = Pr(30 days) + Pr(31 days) + Pr(32 days) + ..... where:

    Pr(30 days) = (0.999^30)(0.001) (why?)

    Pr(31 days) = (0.999^31)(0.001) (why?)

    etc.

    You now have an infinite geometric series, and the formula for finding such a sum is well known.
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    Pr(at least 30 days) = Pr(30 days) + Pr(31 days) + Pr(32 days) + ..... where:

    Pr(30 days) = (0.999^30)(0.001) (why?)

    Pr(31 days) = (0.999^31)(0.001) (why?)

    etc.

    You now have an infinite geometric series, and the formula for finding such a sum is well known.
    The answer just comes out to 0.999^{30}, the same as by using SpringFan25's reasoning.
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