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At a car and truck dealership, the probability that a vehicle is white is 0.25. The probability that it is a pickup truck is 0.15. The probability that it is a white pickup truck is 0.06.

What is the probability that a vehicle is white, given that the vehicle is a pickup truck? Round your answer to two decimal places.

A. 0.06
B. 0.40
C. 0.19
D. 0.24

Sagot :

GinnyAnswer
To find the probability that a vehicle is white given that the vehicle is a pickup truck, we need to use the concept of conditional probability. The conditional probability formula is:

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

Where [tex]\( P(A|B) \)[/tex] is the probability of event A occurring given that event B has occurred. In this context:

- [tex]\( A \)[/tex] is the event that a vehicle is white.
- [tex]\( B \)[/tex] is the event that a vehicle is a pickup truck.

Given:
- [tex]\( P(white) = 0.25 \)[/tex]
- [tex]\( P(pickup\ truck) = 0.15 \)[/tex]
- [tex]\( P(white\ \cap\ pickup\ truck) = 0.06 \)[/tex] (the probability that the vehicle is both white and a pickup truck)

The conditional probability [tex]\( P(white|pickup\ truck) \)[/tex] is calculated as follows:

[tex]\[ P(white|pickup\ truck) = \frac{P(white\ \cap\ pickup\ truck)}{P(pickup\ truck)} \][/tex]

Substituting the given probabilities into the formula:

[tex]\[ P(white|pickup\ truck) = \frac{0.06}{0.15} \][/tex]

Simplifying the fraction:

[tex]\[ P(white|pickup\ truck) = 0.4 \][/tex]

Therefore, the probability that a vehicle is white, given that the vehicle is a pickup truck, is:

[tex]\[ \boxed{0.4} \][/tex]

So, the correct answer is not listed among the choices provided (A-D). The correct probability, rounded to two decimal places, is 0.40 or 0.4.
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