Question

Papa's Italian Restaurant has collected data about customer sauce orders. It calculated that P(marinara) = 0.74, P(pesto) = 0.62, and P(marinara or pesto) = 0.90. Determine the P(marinara and pesto).

0.12

0.46

0.16

0.22

Answer 1

Let the event 'has marinara' be M and let the event 'has pesto' be P.
\[P(M \cup P)=P(M)+P(P)-P(M \cap P)\ ........(1)\]
Plugging in the given values of probability into (1), we get:
\[0.9=0.74+0.62-P(M \cap P)\ ..........(2)\]
So now you just need to solve equation (2) to find the required intersection of marinara and pesto.

Answer 2

So the answer is .46, I believe. That's what my original thought was but I kept second guessing myself. Am I right?

Answer 3

Yes, 0.46 is the solution.

Answer 4

thank you

Answer 5

You're welcome :)