poisson distribution

**tanjir** · November 23rd 2008, 11:36 PM

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

**mr fantastic** · November 24th 2008, 03:19 AM

Originally Posted by tanjir

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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