Thread: 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

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:

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

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