Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
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.
[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.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.