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8 November, 20:46

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).

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  1. 8 November, 21:06
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    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.
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