Question

an engineering company has four openings and the applicant pool consists of five database administrators and eight network engineers. if the hiring is done without regard for the specific qualifications of the applicants, find the probability that the four hired will be
(a) all network engineers. round your answer to five decimal places.
the probability that the four people hired will be all network engineers is

Explanation:

Step1: Calculate total number of applicants

There are \(5\) database administrators and \(8\) network engineers. So total applicants \(n=5 + 8=13\).

Step2: Use combination formula

The number of ways to choose \(4\) people out of \(13\) is \(C(n,k)=\frac{n!}{k!(n - k)!}\), where \(n = 13\) and \(k=4\). So \(C(13,4)=\frac{13!}{4!(13 - 4)!}=\frac{13\times12\times11\times10}{4\times3\times2\times1}=715\).
The number of ways to choose \(4\) network engineers out of \(8\) is \(C(8,4)=\frac{8!}{4!(8 - 4)!}=\frac{8\times7\times6\times5}{4\times3\times2\times1}=70\).

Step3: Calculate probability

Probability \(P=\frac{C(8,4)}{C(13,4)}\). Substitute the values: \(P=\frac{70}{715}\approx0.098\).

Answer:

\(0.098\)