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).

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.