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Math Help - poisson distribution

  1. #1
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    Smile poisson distribution

    when a large number of flash lights leaving a factory is inspected it is found that the bulb is faulty in 1% of the flash lights and the switch is faulty in 1.5% of them.Assuming that the faults occur independently and at random,find
    a)the probability that a sample of 80 flash lights contains at least one flash lights with both a defective bulb and a defective switch.



    ans:0.0119.
    please help me
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  2. #2
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    Quote Originally Posted by tanjir View Post
    when a large number of flash lights leaving a factory is inspected it is found that the bulb is faulty in 1% of the flash lights and the switch is faulty in 1.5% of them.Assuming that the faults occur independently and at random,find
    a)the probability that a sample of 80 flash lights contains at least one flash lights with both a defective bulb and a defective switch.



    ans:0.0119.
    please help me
    Using the Poisson approximation to the binomial distribution:

    \lambda = (0.01)(0.015)(80) = 0.012.

    \Pr(X \geq 1) = 1 - \Pr(X = 0) = 1 - \frac{e^{-0.012} \, (0.012)^0}{0!} = 1 - e^{-0.012} = 0.0119 (approximation correct to 4 decimal places).
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