Question

A container contains 15 diesel engines. The company chooses 13 engines at random, and will not ship the container if any of the engines chosen are defective. Find the probability that a container will be shipped even though it contains 2 defectives if the sample size is 13.

The Probability the container will be shipped is
Round to the nearest thousandth as needed

Answer 1

Explanation:

We have 15 diesel engines, from which 13 are okay, and 2 are defected. Since there are 15 engines and 13 will be chosen two ship in the continer, the possibe number of outcomes is:

`C(n,r) = (n!)/(r!(n-r)!)`

Where n = 15 and r=11.

Substituting, we find that:

`C(15,11) = (15!)/(13!(15-13)!) = (15!)/(13!2!) = 105`

Now we need to find the probability of choosing 13 effective engines and 0 defective engines, which is given by:

`C(13,13) C(2,0) = (13!)/(13!0!) (2!)/(0!2!) = 1`

The probability of shipping the container is:
`(1)/(105)`