A manufacturing plant produces a special kind of lightbulb. each light bulb produced has a 0.040 probability of being defective. five light bulbs are chosen at random from the production line. to the nearest thousandth, what is the probability that exactly two of the five bulbs will be defective?

Question

Mathematics

Damian Johns

5 January, 22:54

A manufacturing plant produces a special kind of lightbulb. each light bulb produced has a 0.040 probability of being defective. five light bulbs are chosen at random from the production line. to the nearest thousandth, what is the probability that exactly two of the five bulbs will be defective?

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Haiden Mcmahon · Answer 1

Using the Binomial distribution formula, the probability that exactly 2 bulbs are defective will be given by:

P (x) = n! / ((n-x) ! x!) p^x (1-p) ^ (n-x)

n=5, x=3, p=0.04

plugging our values we obtain:

P (x) = 5! / (3!2!) * 0.04^2*0.96^3

P (x) = 0.0142