Question

Suppose the probability that a lightbulb is defective is 0.1.

What is the probability that if you select a random sample of 8 lightbulbs, exactly 2 of the 8 lightbulbs will be defective?

I know what the answer should be please explain how you got to it

Answer 1

Solution:

We are given that: the probability that a lightbulb is defective is 0.1

Thus p = probability that a lightbulb is defective = 0.1

We have to find the probability that if you select a random sample of 8 lightbulbs, exactly 2 of the 8 lightbulbs will be defective.

That is we have to find: P( X = 2) = ..........?

n =sample size = 8

X = number of defective lightbulbs follows Binomial distribution with n = 8 and p = 0.1

Thus using Binomial probability distribution:

where

and q = 1 - p = 1 - 0.1 = 0.9

Thus