Question

Angelina's Italian Restaurant has collected data about customer sauce orders. It calculated that P(pesto) = 0.42, P(alfredo) = 0.86, and P(pesto or alfredo) = 0.93. Determine the P(pesto and alfredo).

0.35
0.07
0.51
0.23

Please someone help me. Thank you.

Answer 1

You could cheat and just use the addition rule:

P(A or B) = P(A) +P(B) - P(AB)

So:

.93 = .42 + .86 - P(AB)

P(AB) = .42 + .86 - .93

P(AB) = .35

Thus: P(apesto and alfredo) = 0.35

Answer 2

Answer: 0.35

Explanation:

Given: P(pesto) = 0.42, P(alfredo) = 0.86, and P(pesto or alfredo) = 0.93.

We know that for events A and B,

`\text{P(A or B)=P(A)+P(B)-P(A and B)}`

Therefore, for the given situation, we have

`\text{P(pesto or alfredo) =P(pesto)+P(alfredo)-P(pesto and alfredo)}\\\\\Rightarrow0.93=0.42+0.86-\text{P(pesto and alfredo)}\\\\\Rightarrow\text{P(pesto and alfredo)}=1.28-0.93\\\\\Rightarrow\text{P(pesto and alfredo)}=0.35`