Question

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).
@mathmale

Answer 1

Here's another case where we need to know a number of concepts and formulas to be able to calculate a probability.
Are you familiar with Venn diagrams?
With the operator "OR"?
with the operator "AND"?

Answer 2

a two way table?

Answer 3

Two way tables are great, but apply primarily to "conditional probability." I'm experimenting to see whether I can piece together a solution for the problem at hand.

Answer 4

ok i really need to fasten my speed

Answer 5

This probability is a major topic that will almost surely show up on any test. What strategies do you normally use to learn the vocabularies and formulas of topics such as "joint probability," "intersection," "union," and so on? I could simply type out an answer, but that answer would mean little unless you were familiar with these terms.

Answer 6

Do you happen to have a probability and statistics textbook with you?

Answer 7

yes

Answer 8

woohoo works part time in a pizza factory and knows from experience that marinara pizza is most popular, followed by alfredo. But some strange people order pizza with both marinara sauce and alfredo sauce.

Answer 9

.82/.96

Answer 10

We'd write the relevant probabilities like this:
P(M)=0.82
P(A)=0.76
P(A OR M)=0.96
We want P(A AND M)

Answer 11

Have you seen this terminology/symbolism before?

Answer 12

\[p(a \cup m)\]

Answer 13

yes i have

Answer 14

Great. That's the same thing as my P(A OR M).

For this situation, you want to calculate the probability that a customer will order both marinara and alfredo sauce on his/her pizza.

The relevant formula is P(A OR M) = P(A) + P(M) - P(A AND M).

Answer 15

Which of these do we already know, and what are their values (if known)?

P(A OR M)
P(A)
P(M)
P(M AND A)

Answer 16

is it 85%

Answer 17

Would you mind typing out the method you used to obtain 85%?

BRB

Answer 18

\[p(a \cup b) /p(b)\]

Answer 19

Here's what I've done. I'll first write out the formula, and then insert the appropriate values.

Answer 20

P(A u B) = P(a) + P(b) - P( a AND

Answer 21

b).

Answer 22

In this problem we want P(A AND B), agreed?

Answer 23

sorry i made a mistake is it 0.62

Answer 24

pls math male i really need to get this going pls tell me if im right

Answer 25

Yes, that is correct. This time I won't put you on the spot asking you to show how you got that result, but yes, you've done the right thing and are finished with this problem.

Answer 26

Thank You!!!

Answer 27

Let's look at what we did to find that result:
We looked carefully at the given info. We saw we had a formula for P(A u B) and needed a value for P(A AND B).
So

Answer 28

we looked up these formulas in woohoo's textbook and found
P(A u B)=P(a) + P(b) - P(a AND b).
We substituted the known values and found that the unknown quantity, P(a AND b), is at the right. Simple arithmetic produces the correct value for P(A AND B).

Answer 29

The more you practice doing this kind of problem, always taking notes and explaining to yourself what the formulas represent and what they're for, the better you'll do in this course.

Answer 30

I just did what you said and looked at the examples in the book and followed it through with this question

Answer 31

Great. Hope you'll take notes on this work and thus have something to study later on when you have a test or more homework coming up.

Answer 32

Thankyou both of of you smmm the answer was 0.62!