Question

when randomly selecting adults, let m denote the event of randomly selecting a male and let b denote the event of randomly selecting someone with blue eyes. what does p(m|b) represent? is p(m|b) the same as p(b|m)? what does p(m|b) represent? a. the probability of getting a male or getting someone with blue eyes. b. the probability of getting someone with blue eyes, given that a male has been selected. c. the probability of getting a male and getting someone with blue eyes. d. the probability of getting a male, given that someone with blue eyes has been selected.

Explanation:

To determine what \( P(M|B) \) represents, we recall the definition of conditional probability. The notation \( P(A|B) \) means the probability of event \( A \) occurring given that event \( B \) has already occurred. Here, \( A = M \) (selecting a male) and \( B = B \) (selecting someone with blue eyes). So \( P(M|B) \) is the probability of selecting a male, given that the person selected has blue eyes.

• Option A is incorrect because it describes \( P(M \cup B) \) (probability of male or blue eyes).
• Option B is incorrect because it describes \( P(B|M) \) (probability of blue eyes given male).
• Option C is incorrect because it describes \( P(M \cap B) \) (probability of male and blue eyes).
• Option D matches the definition of \( P(M|B) \).

Answer:

D. The probability of getting a male, given that someone with blue eyes has been selected.