Question

A container contains 1212 diesel engines. The company chooses 88 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 88.

Answer 1

The probability that a container will be shipped even though it contains 2 defectives if the sample size is 88, will be
`P(S)=85.99\%`

Explanation:

The first step is to count the number of total possible random sets of taking a sample size of 88 engines over 1212 engines of the population, so
`\left[\begin{array}{ccc}1212\\88\end{array}\right] =1212C88=4.7205x10^(135)`

The second step is to count the number of total possible random sets of taking a sample size of 88 engines over 1210 engines (discounting the 2 defective engines) as the possible ways to succeed, so
`\left[\begin{array}{ccc}1210\\88\end{array}\right] =1212C88=4.0596x10^(135)`

Finally we need to compute
`(\# ways\ to\ succeed)/(\# random\ sets\ of \ 88) =(4.0596x10^(135))/(4.7205x10^(135))=0.8599=P(S)`, therefore the probability that a container will be shipped is
`P(S)=85.99\%`