Question

The mathematics faculty at a college consists of 7 professors, 8 associate professors, 6. assistant professors, and 4 instructors. If one faculty member is randomlyselected, find the probability of choosing a professor or an instructorThe probability is . (Type an integer or a fraction. Simplify your answer)

Answer 1

Answer:

Let the number of professors be represented with the letter P

$n(P)=7$

Let the number of associate professors be represented by the letter A

$n(A)=8$

Let the number of assistant professors be represented by the letter S

$n(S)=6$

Let the number of instructors be represented by the letter I

$n(I)=4$

The total number of sample space will be calculated below as

$\begin{gathered} n(T)=n(P)+n(A)+n(S)+n(I) \\ n(T)=7+8+6+4 \\ n(T)=25 \end{gathered}$

To figure out the probability of choosing a professor or an instructor, we will use the formula below

$Pr(PorI)=Pr(P)+Pr(I)$$Pr(P)=\frac{n(P)}{n(T)}=\frac{7}{25}$$Pr(I)=\frac{n(I)}{n(T)}=\frac{4}{25}$

By substituting the values, we will have

$\begin{gathered} Pr(PorI)=Pr(P)+Pr(I) \\ Pr(PorI)=\frac{7}{25}+\frac{4}{25} \\ Pr(PorI)=\frac{11}{25} \end{gathered}$

Hence,

The final answer is

$\Rightarrow\frac{11}{25}$