To find the correct answer, we'll use the definitions of probability:
- P(A) represents the probability of selecting a male randomly.
- P(A|B) represents the probability of selecting a male randomly given that the person has brown eyes.
Without knowing the actual values of these probabilities, we can still infer some relationships based on the given options:
Option A: P(A) = 0.6, P(A|B) = 0.5
Option B: P(A) = 0.6, P(A|B) = 0.6
Option C: P(A) = 0.5, P(A|B) = 0.6
Option D: P(A) = 0.17, P(A|B) = 0.5
Now, let's analyze these options:
Option A: P(A) = 0.6, P(A|B) = 0.5
This option implies that the probability of selecting a male randomly is 0.6, and given that the person has brown eyes, the probability of selecting a male is 0.5. However, it's important to note that the probability of selecting a male should not decrease when we consider the additional information of having brown eyes. Therefore, Option A is not correct.
Option B: P(A) = 0.6, P(A|B) = 0.6
This option implies that the probability of selecting a male randomly is 0.6, and given that the person has brown eyes, the probability of selecting a male is also 0.6. This relationship is plausible because the probability of selecting a male should not change significantly based on the eye color. Therefore, Option B could be a correct answer.
Option C: P(A) = 0.5, P(A|B) = 0.6
This option implies that the probability of selecting a male randomly is 0.5, and given that the person has brown eyes, the probability of selecting a male is 0.6. However, based on Option B's plausible relationship, Option C seems less likely, as the probability of selecting a male should not be higher when we consider the additional information of having brown eyes. Therefore, Option C is less likely to be the correct answer.
Option D: P(A) = 0.17, P(A|B) = 0.5
This option implies that the probability of selecting a male randomly is 0.17, and given that the person has brown eyes, the probability of selecting a male is 0.5. However, the probability of selecting a male should not increase that much when we consider the additional information of having brown eyes. Therefore, Option D is not correct.
Based on our analysis, the most plausible answer is Option B: P(A) = 0.6, P(A|B) = 0.6. This means the probability of selecting a male randomly is 0.6, and given that the person has brown eyes, the probability of selecting a male remains 0.6.