rebecca101
contestada

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.

Respuesta :

backseatdog
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
JeanaShupp

Answer: 0.35

Step-by-step 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,

[tex]\text{P(A or B)=P(A)+P(B)-P(A and B)}[/tex]

Therefore, for the given situation, we have

[tex]\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[/tex]

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