Question

This Venn diagram shows the pizza topping preferences for 9 students. Let event A = The student likes pepperoni. Let event B = The student likes olives. What is P(A or B)?​

Answer 1

`P(A\ or\ B)=(7)/(9)`

Explanation:

We need to use the formula to calculate the probability of (A or B) where

A=Probability a student likes pepperoni

B=Probability a student likes olive

A and B =Probability a student likes both toppings in a pizza

A or B =Probability a student likes pepperoni or olive (and maybe both), a non-exclusive or

The formula is

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

Since 6 students like pepperoni out of 9:

`P(A) = (6)/(9)`

Since 4 students like olive out of 9:

`P(B) = (4)/(9)`

Since 3 students like both toppings out of 9

`P(A\ and\ B) = (3)/(9)`

Then we have

`P(A\ or\ B)=(6)/(9)+(4)/(9)-(3)/(9)`

`P(A\ or\ B)=(7)/(9)`