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Let event A be defined as a male being randomly selected. Let event B be defined as a person with brown eyes being

randomly selected.
Find P(A) and P(A|B).
A. P(A)=0.6, P(A|B) = 0.5
B. P(A)=0.6, P(A|B) = 0.6
C. P(A)=0.5, P(A|B) = 0.6
D. P(A) = 0.17, P(A|B)=0.5

Let event A be defined as a male being randomly selected. Let event B be defined as-example-1
User Highstakes
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1 Answer

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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.

User Ben Evans
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