Question

there are 40 employees that are in a certain firm. we know that 24 of these employees are male, 2 of these males are secretaries, and 10 secretaries are employed by The firm. What is the probability that an employee chosen at random is a secretary, given that this person is a female?

Answer 1

The number of employees=40

Male employees=24

Female employees=40-24=16

Total secretaries employed by the firm=10

Male secretaries=2

Female secretaries=10-2=8

To find the probability that an employee chosen at random is a secretary, given that this person is a female,

probability of females out of total employees is ,

$\frac{16}{40}$

The probability that female employees who are secretaries is,

$\frac{8}{40}$

The required probability is given by,

$\begin{gathered} P_{}=\frac{\frac{8}{40}}{\frac{16}{40}} \\ =\frac{8}{40}.\frac{40}{16} \\ =0.5 \end{gathered}$