Question

The mathematics department of a college has 8 male professors , 11 female professors 5 male teaching assistants , and 5 female teaching assistants . If a person is selected at random from the group , find the probability that the selected person is a professor or a male

Answer 1

The probability that the selected person is a professor or a male is;

`(24)/(29)`

Step-by-step explanation:

Given that the mathematics department of a college has 8 male professors, 11 female professors 5 male teaching assistants, and 5 female teaching assistants.

let A represent professors and B represent males.

the probability that the selected person is a professor or a male is;

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

Solving or the probability that the selected person is a professor;

`P(A)=(n(A))/(n(T))=\frac{\text{number of professors}}{\text{total number of persons}}`
`P(A)=(8+11)/(8+11+5+5)=(19)/(29)`

The probability that the selected person is a male is;

`P(B)=(n(B))/(n(T))=\frac{\text{ number of males }}{\text{ Total number of persons}}`
`P(B)=(8+5)/(8+11+5+5)=(13)/(29)`

Then the probability that the selected person is a male and a professor;

`P(A\cap B)=(n(A\cap B))/(n(T))=\frac{\text{ number of male professors}}{\text{total number of persons}}`
`P(A\cap B)=(8)/(8+11+5+5)=(8)/(29)`

We can now substitute to get the probability that the selected person is a professor or a male;

`\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=(19)/(29)+(13)/(29)-(8)/(29) \\ P(A\cup B)=(19+13-8)/(29) \\ P(A\cup B)=(24)/(29) \end{gathered}`

Therefore, the probability that the selected person is a professor or a male is;

`(24)/(29)`