Question

In school, there are 800 students and 80 faculty members. 500 students and 50faculty members are males. If a person is selected at random, then find theprobability that the selected person is a faculty member or a female.

Answer 1

For non-mutually exclusive events, the probability can be calculated using the formula

`P(A\text{ or B) = P(A) + P(B) - P(A }\cap B)`

Let's take

A = Faculty Member

B = Female

The probability of A will be

`P(A)=(80)/(880)`

The probability of B will be

`P(B)=(330)/(880)`

The probability of (A n B), that is, the number of faculty members that are females, will be

`P(A\cap B)=(30)/(880)`

Therefore, the probability will be calculated as

`\begin{gathered} P(\text{A or B) }=\text{ }(80)/(880)+(330)/(880)-(30)/(880) \\ =(380)/(880) \\ =0.432 \end{gathered}`

The probability is 0.43.