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.
Accepted Solution
A:
Answer:The probability that a container will be shipped even though it contains 2 defectives if the sample size is 88, will be [tex]P(S)=85.99\%[/tex]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 [tex]\left[\begin{array}{ccc}1212\\88\end{array}\right] =1212C88=4.7205x10^{135}[/tex]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 [tex]\left[\begin{array}{ccc}1210\\88\end{array}\right] =1212C88=4.0596x10^{135}[/tex]Finally we need to compute [tex]\frac{\# ways\ to\ succeed}{\# random\ sets\ of \ 88} =\frac{4.0596x10^{135}}{4.7205x10^{135}}=0.8599=P(S)[/tex], therefore the probability that a container will be shipped is [tex]P(S)=85.99\%[/tex]