0.0398
0.0389
0.0368
0.0396
Answer is Right!
Answer is Wrong!
The correct answer is $\boxed{\text{B. }0.0389}$.
The probability that a person subscribes to automotive magazine given that they own a sports car is denoted by $P(S|C)$. We can calculate this probability using Bayes’ theorem:
$$P(S|C) = \frac{P(C|S)P(S)}{P(C)}$$
We are given that $P(C|S) = 0.4$, $P(S) = 0.03$, and $P(C) = 0.03 + 0.3 = 0.33$. Substituting these values into Bayes’ theorem, we get:
$$P(S|C) = \frac{(0.4)(0.03)}{(0.33)} = 0.0389$$
Therefore, the probability that a person subscribes to automotive magazine given that they own a sports car is $\boxed{\text{B. }0.0389}$.
Here is a brief explanation of each option:
- Option A: $0.0398$. This is the probability that a person owns a sports car given that they subscribe to automotive magazine. This is not the probability that a person subscribes to automotive magazine given that they own a sports car.
- Option B: $0.0389$. This is the correct answer.
- Option C: $0.0368$. This is the probability that a person does not own a sports car given that they subscribe to automotive magazine. This is not the probability that a person subscribes to automotive magazine given that they own a sports car.
- Option D: $0.0396$. This is the probability that a person owns a sports car. This is not the probability that a person subscribes to automotive magazine given that they own a sports car.