One hundred employees of a company are asked how they get to work and whether they work full time or part time. The table below shows the results. If one of the 100 employees is randomly selected, find the probability of getting someone who carpools or someone who works full time.

Full time Part time

Public Transportation 7 10

Bicycle 4 3

Drive alone 30 31

Carpool 6 9

The probability is 56/100, or 14/25 = 0.56.

These events are not mutually exclusive, meaning they can happen at the same time. This means we use

P (A or B) = P (A) + P (B) - P (A and B)

P (carpool or full time) = P (carpool) + P (full time) - P (carpool & full time)

There are 6+9=15 people out of 100 that carpool.

There are 7+4+30+6=47 people out of 100 that work full time.

There are 6 people out of 100 that carpool and work full time.

This gives us

15/100 + 47/100 - 6/100 = 56/100