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Math Help - please help

  1. #1
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    please help

    A lamp has two bulbs, each of a type with an average lifetime of 4 hours. The probability density function for the lifetime of a bulb is .
    What is the probability that both of the bulbs will fail within 4 hours?
    i took the douple integral of this function with bounds from 0 to 4 and got the answer 1 which isn't right where did i go wrong?
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  2. #2
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    Quote Originally Posted by koalamath View Post
    A lamp has two bulbs, each of a type with an average lifetime of 4 hours. The probability density function for the lifetime of a bulb is .
    What is the probability that both of the bulbs will fail within 4 hours?
    i took the douple integral of this function with bounds from 0 to 4 and got the answer 1 which isn't right where did i go wrong?
    Are the lifetimes of each bulb independent of each other? If so:

    \Pr(T < 4) = \int_{0}^{4} \frac{1}{4} e^{-t/4} \, dt = 1 - \frac{1}{e}.

    Therefore the probability of both bulbs failing within 4 hours is \left(1 - \frac{1}{e}\right) \cdot \left(1 - \frac{1}{e}\right) = .....
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  3. #3
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    Thank you!
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