Question

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).

Answer 1

I'm not understanding this, if .89 is both than i figure the marinara and alfredo would be 11% or .11 but that's not one of the answers

Answer 2

P(m and a) = P(m) + P(a) - P(m or a)
Use that relationship to solve your problem.

Answer 3

That's a general relationship that is always true.
It doesn't matter what A and B are
Pr(A and B) = Pr(A) + Pr(B) - Pr(A or B)
and
Pr(A or B) = Pr(A) + Pr(B) - Pr(A and B)

Answer 4

Uhm, that doesn't make sense. Could you explain? If P (m+a)= .89 then doing P(m or A) lets say A would just leave me with the original m

Answer 5

Or is that not how it works?

Answer 6

I was just about to draw something like the above.

Answer 7

OOOH okay so taking away the B from B & A would only take away the B included in A?

Answer 8

Yes, it makes sense when you look at the diagram.
Just tuck this formula away for future use , though, so you don't have to derive it every time\
Pr(A and B) = Pr(A) + Pr(B) - Pr(A or B)
and
Pr(A or B) = Pr(A) + Pr(B) - Pr(A and B)\
It is VERY useful

Answer 9

So what answer do you get for your problem?

Answer 10

I got .31 or 31%

Answer 11

Is this correct? o:

Answer 12

yes. that's what i got, too

Answer 13

cool! Thank you! ^_^

Answer 14

No problem