Question

(09.03)

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).

0.33

0.60

0.31

0.68

Answer 1

@kirbykirby @satellite73
Can anyone help walk me through this one?

Answer 2

\[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]

Answer 3

So let's abbreviate, M = marinara, A = alfredo
What they tell you is:
\(P(M) = 0.64\\
P(A)= 0.56\\
P(M \text{ or }A)=P(M \cup A)=0.89\)

They want \(P(M \text{ and } A)=P(M \cap A)\)

Use the rule:
\(P(M \cup A ) = P(M) + P(A) - P(M \cap A)\)

Answer 4

Ok give me just a minute

Answer 5

or in @kirbykirby notation \[P(M\cap A)=P(M)+P(A)-P(M\cup A)\] when you solve for what you are looking for

Answer 6

You are solving for p(mUa). ?

Answer 7

Upside down u I mean (intersection)

Answer 8

yes

Answer 9

\cup is \(\cup\) union
\cap is \(\cap\) intersection if you want to write it

Answer 10

Ok so it is p(MUA)=P(0.64)+P(0.56)-P(0.89)

Answer 11

So P(MUA)=0.31 @kirbykirby

Answer 12

yup !

Answer 13

Thank you