Question

Pizza Time has collected data about customer pizza topping preferences. They have calculated that P(pepperoni) = 0.7, P(olives) = 0.6, and P(pepperoni or olives) = 0.8. Determine the P(pepperoni and olives).
@Disco619 @math&ing001

Answer 1

@ikram002p

Answer 2

@mathmale

Answer 3

It is entirely possible (even probable) that some customers will want their pizza with pepperoni AND olives, so that means that the events "customer prefers olives" and "customer prefers pepperoni" do overlap. Our job is to find the probability of such overlap. I'll denote that as P(pepperoni AND olives).

When the events "customer prefers olives" and "customer prefers pepperoni" can partially overlap, then the formula

P(olives OR pepperoni) = P(olives) + P(pepperoni) - P(pepperoni AND olives) applies.

Simply substitute the given values of the first three probabilities to obtain P(pepperoni AND olives).

Answer 4

1.3?

Answer 5

@mathmale

Answer 6

@phi

Answer 7

woohoo: Whoo Hoo! Remember that probabilities MUST lie between 0 and 1, so 1.3 is automatically out the door.

Mind trying again?

Your job is to find P(olives AND pepperoni), given P(olives), P(pepperoni) and P(olivers OR pepperoni. Make certain that you have the relevant formulas in front of you. See my previous comments.

Answer 8

P(olives OR pepperoni) = P(olives) + P(pepperoni) - P(pepperoni AND olives) applies.

Answer 9

0.6? @mathmale

Answer 10

P(olives OR pepperoni) = P(olives) + P(pepperoni) - P(pepperoni AND olives) applies.

This translates into:

0.8 = 0.6 + 0.7 - P(pepp AND olives).

Solve that for P(pepp AND olives). Note that

0.8 = 1.3 - P(pepp AND olives)

Answer 11

.8=.5

Answer 12

I think you meant 1.3 - 0.8 = 0.5. That is correct. 0.8 = 0.5 is never correct.

So, you're essentially done solving this problem.

Answer 13

Thank You!

Answer 14

You're welcome! and I apologize for my slow responses.