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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?

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carlosego

Answer:

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

Step-by-step explanation:

Let's call

[tex]P_p[/tex] = the proability of someone asking for a pizza

[tex]P_s[/tex] = 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:

[tex]P_p[/tex] = 70% = 0.7

[tex]P_s[/tex] = 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 = [tex]P_p[/tex] ∪ [tex]P_s[/tex] - 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%

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