Question

A package contains 12 resistors, 3 of which are defective. If 4 are selected, find the probability of getting

Answer 1

Incomplete question, but I gave a primer on the hypergeometric distribution, which is used to solve this question, so just the formula has to be applied to find the desired probabilities.

Explanation:

The resistors are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

`P(X = x) = h(x,N,n,k) = (C_(k,x)*C_(N-k,n-x))/(C_(N,n))`

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

`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)!)`

In this question:

12 resistors, which means that
`N = 12`

3 defective, which means that
`k = 3`

4 are selected, which means that
`n = 4`

To find an specific probability, that is, of x defectives:

`P(X = x) = h(x,N,n,k) = (C_(k,x)*C_(N-k,n-x))/(C_(N,n))`

`P(X = x) = h(x,12,4,3) = (C_(3,x)*C_(9,4-x))/(C_(12,4))`