Nanna's Italian Restaurant has collected data about customer sauce orders. It calculated that P (marinara) = 0.64, P (alfredo) = 0.56, and P (marinara or alfredo) = 0.89. Determine the P (marinara and alfredo).

To answer this question, apply this formula P (m and a) = P (m) + P (a) - P (m or a). Where m stands for marinara and a stands for alfredo.

P (m and a) = P (m) + P (a) - P (m or a)

P (m and a) = 0.64 + 0.56 - 0.89

P (m and a) = 0.31

Given the probabilities of individual events to occur, for the conjunction "and"

P (marinara and alfredo) = P (marinara) x P (alfredo) = 0.64 + 0.59 = 0.3776

Now for the first question, P (marinara or alfredo), use the equation,

= P (marinara) + P (alfredo) - P (marinara and alfredo)

Substituting,

= 0.64 + 0.56 - 0.3776 = 0.8224