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.
