Question

Mama's Italian Restaurant has collected data about customer sauce orders. It calculated that P(marinara) = 0.82, P(alfredo) = 0.76, and P(marinara or alfredo) = 0.96. Determine the P(marinara and alfredo).

Answer 1

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Let A be the event that customer orders Marinara sauce and B be the event that customer orders Alfredo sauce.

So,

P(A) = 0.82

P(B) = 0.76

P(A ∪ B) = 0.96

We are to find P(A ∩ B). Using the values in above formula we get:

0.96 = 0.82 + 0.76 - P(A ∩ B)

⇒

P(A ∩ B) = 0.62

Thus the probability that customer orders Marinara and Alfredo Sauce is 0.62.

Answer 2

For two events A and B,

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Let A be the event that customer orders Marinara sauce and B be the event that customer orders Alfredo sauce.

So,
P(A) = 0.82
P(B) = 0.76
P(A ∪ B) = 0.96
We are to find P(A ∩ B). Using the values in above formula we get:

0.96 = 0.82 + 0.76 - P(A ∩ B)
⇒
P(A ∩ B) = 0.62

Thus the probability that customer orders Marinara and Alfredo Sauce is 0.62.