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

Answer:

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

Step-by-step 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 $\frac{\# ways\ to\ succeed}{\# random\ sets\ of \ 88} =\frac{4.0596x10^{135}}{4.7205x10^{135}}=0.8599=P(S)$, therefore the probability that a container will be shipped is $P(S)=85.99\%$