Question

At a pizza shop, 70% of the customers order a pizza, 25% of the customers order a salad, and 15% of the customers order both a pizza and a salad. If a customer is chosen at random, what is the probability that he or she orders either a pizza or a salad?

Answer 1

The probability that a randomly selected customer orders a pizza or a salad is 80%

Explanation:

Let's call

`P_p` = the proability of someone asking for a pizza

`P_s` = the probability that a customer orders a salad

Pp∩s = the probability that a customer orders a pizza and a salad.

We know from the statement of the problem that:

`P_p` = 70% = 0.7

`P_s` = 25% = 0.25

Pp∩s = 15% = 0.15

We want to know the probability that a randomly selected customer will order a pizza or a salad. Then, by set theory, that probability is calculated as:

Pp∪s =
`P_p` ∪
`P_s` - Pp∩s

So:

Pp∪s = Pp + Ps - Pp∩s

Where Pp∪e is the probability that the customer orders a pizza or a salad, but not both at the same time.

Pp∪e = 0.7 + 0.25 -0.15

Pp∪e = 0.8

Finally, the probability that a randomly selected customer orders a pizza or a salad is 80%