A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. What is the probability that a randomly selected customer will get the classic wash and vacuum their car?
A) 0.05
B) 0.09
C) 0.12
D) 0.25

Using conditional probability, it is found that the probability that a randomly selected customer will get the classic wash and vacuum their car is:

B) 0.09

Conditional Probability

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.

In this problem:

Event A: Classic wash.
Event B: Vacuum.

35% get the classic wash, hence [tex]P(A) = 0.35[/tex].
Of those who get the classic wash, 25% vacuum their cars, hence [tex]P(B|A) = 0.25[/tex]

Then:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(B|A)P(A)[/tex]

[tex]P(A \cap B) = 0.25(0.35)[/tex]

[tex]P(A \cap B) = 0.0875[tex]

Close to 0.09, hence option B.

A similar problem is given at https://brainly.com/question/14398287