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).

Answer 1

Here's what we know:

There's a 0.42 chance someone will order pesto.
There's a 0.86 chance someone will order alfredo.
There's a 0.93 chance someone will order pesto or alfredo.

So what's the chance that someone ordered both?
Well, subtract 0.86 from 0.93 and you'd get 0.07.
That's the chance someone will order only pesto.
The rest of the 0.42 must have been from those who had both.
0.42 minus 0.07 is 0.35.

Answer 2

Answer:

Use the formula:

Let A and B be two events.

$P(A \cup B) = P(A)+P(B)-P(A \cap B)$

As per the statement:

Angelina's Italian Restaurant has collected data about customer sauce orders.

P(pesto) = 0.42

P(alfredo) = 0.86 and

P(pesto or alfredo) =0.93

We have to find  the P(pesto and alfredo).

Apply the given formula we have;

P(pesto or alfredo) = P(pesto)+P(alfredo)-P(pesto and alfredo)

Substitute the given values we have;

0.93 = 0.42+0.86-P(pesto and alfredo)

⇒0.93 = 1.28-P(pesto and alfredo)

then;

P(pesto and alfredo) = 1.28-0.93= 0.35

Therefore, the value of P(pesto and alfredo) is, 0.35