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).

A.0.5

B.0.6

C. 0.7

Answer 1

The answer would be 0.5. This is because the sum off Olives and Pepperoni is 0.13 and the number of those people who choose Pepperoni or Olives is only 0.8. Thus, the remaining number is now on Pepperoni and olives.

Answer 2

Option A is correct that is
`.5=P(A\capB)`

Explanation:

We have given probabilities

P(pepperoni)=0.7

P(olives)=0.6

P(pepperoni or olives)=0.8

We need to find the probability of pepperoni and olives

We have a formula

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

Here we have say A is the event of peperroni tha is
`P(A)=0.7`

B is the event of olives that is
`P(B)=0.6`

pepperoni or olives that is is
`P(A\cup B)=0.8`

Pepperoni and olives that is
`P(A\cap B)` we have to find

On substituting the values in the formula we will get

`0.8=0.7+0.6-P(A\cap B)`

`0.8=1.3-P(A\cap B)`

`-.5=-P(A\cap B)`

`.5=P(A\cap B)`

On simplifying the equation we will get

`.5=P(A\cap B)`

Therefore, Option A is correct.