Question

Gavin is a sandwich maker at a local deli. Last week, he tracked the number of peanut butter and jelly sandwiches ordered, noting the flavor of jelly and type of peanut butter requested.
The probability that a sandwich was made with raspberry jelly is 0.84, the probability that it was made with creamy peanut butter is 0.27, and the probability that it was made with raspberry jelly and creamy peanut butter is 0.19.
What is the probability that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter?

Answer 1

Answer:

P(A∪B) = 0.92

Step-by-step explanation:

Let's call A the event that the sandwich was made with raspberry Jelly and B the event that the sandwich was made with creamy peanut butter.

So, the probability P(A∪B) that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is calculated as:

P(A∪B) = P(A) + P(B) - P(A∩B)

Where P(A) is the probability that a sandwich was made with raspberry jelly, P(B) is the probability that it was made with creamy peanut butter and P(A∩B) is the probability that it was made with raspberry jelly and creamy peanut butter.

So, replacing P(A) by 0.84, P(B) by 0.27 and P(A∩B) by 0.19, we get that P(A∪B) is equal to:

P(A∪B) = 0.84 + 0.27 - 0.19

P(A∪B) = 0.92