Question

5. There are 40 employees in a certain firm. We know that 28 of them are male, 2 of these males are secretaries, and 10 secretaries are employed by the firm. What is the probability of the event that an employee chosen at random is a secretary, given that the person is a male?

Answer 1

To determine the asked probability, the first step is to order the information in a contingency table.

We know that the total number of employees of the firm is 40

Of those 28 are male → 2 of them are secretaries

Out of all employees, 10 are secretaries

You have to calculate the probability that the employee is a secretary given that the person is male. You have to concentrate on the information you have about the male employees. And calculate the probability by dividing the number of male secretaries by the number of males employees

`P(S|M)=(2)/(28)=(1)/(14)`

You can express the probability as a percentage

`\begin{gathered} P(S|M)=(1)/(14)\cdot100 \\ P(S|M)=7.14 \end{gathered}`

The probability of choosing one employee at random and the person being a secretary given that is male is 7.14%