Question

The mathematics faculty at a college consists of 12 ​professors, 6 associate​ professors, 9 assistant​ professors, and 8 instructors. If one faculty member is randomly​ selected, find the probability of choosing a professor or an instructor.

Answer 1

Answer:
`(4)/(7)`

Explanation:

P(a) or P(b) = P(a) + P(b)

This means that the probability of a or b is the same of the probability of a plus b

So let's see the probability of a, selecting a professor

`(12)/(12+6+9+8) \\\\(12)/(35)`

We won't simplify just yet so that addition will be easier later

Now let's see the probability of selecting b, an instructor

`(8)/(12+6+9+8) \\\\(8)/(35)`

Now add the 2 probabilities together

`(12)/(35) +(8)/(35) =(20)/(35)`

Simplify.

`(20)/(35) =(4)/(7)`