Question

If the fraction of defective covers produced on the USB Mouse Factory production line is known to be 8%, what is the probability that a sample of 10 covers will contain exactly 2 defectives?

Answer 1

14.78% probability that a sample of 10 covers will contain exactly 2 defectives

Explanation:

For each cover, there are only two possible outcomes. Either it is defective, or it not. The probability of a cover being defective is independent from other covers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

If the fraction of defective covers produced on the USB Mouse Factory production line is known to be 8%, what is the probability that a sample of 10 covers will contain exactly 2 defectives?

This is
`P(X = 2)` when
`p = 0.08, n = 10`. So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 2) = C_(10,2).(0.08)^(2).(0.92)^(8) = 0.1478`

14.78% probability that a sample of 10 covers will contain exactly 2 defectives