Question

The mathematics department of a college has 13 male​ professors, 10 female​ professors, 11 male teaching​ assistants, and 13 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

`(34)/(47)`

Explanation:

GIVEN: The mathematics department of a college has
`13` male​ professors,
`10` female​ professors,
`11` male teaching​ assistants, and
`13` female teaching assistants.

TO FIND: If a person is selected at random from the​ group, find the probability that the selected person is a professor or a male.

SOLUTION:

Total employees in mathematics department
`=47`

Total males in mathematics department
`=24`

Probability that selected person is a male
`=(24)/(47)`

Total professor (male+female)
`=23`

Probability that selected person is professor
`=(23)/(47)`

Total male professor
`=13`

Probability that selected person is a male professor
`=(13)/(47)`

Probability that selected person is a professor or a male
`=(24)/(47)+(23)/(47)-(13)/(47)`

`=(34)/(47)`

Hence probability that selected person is a professor or a male is
`(34)/(47)`