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, given that someone with blue eyes has been selected. b. the probability of getting a male and getting someone with blue eyes. c. the probability of getting someone with blue eyes, given that a male has been selected. d. the probability of getting a male or getting someone with blue eyes. is p(m|b) the same as p(b|m)? a. no, because p(b|m) represents the probability of getting someone with blue eyes, given that a male has been selected. b. yes, because p(b|m) represents the probability of getting a male, given that someone with blue eyes has been selected. c. no, because p(b|m) represents the probability of getting a male, given that someone with blue eyes has been selected. d. yes, because p(b|m) represents the probability of getting someone with blue eyes, given that a male has been selected.

Explanation:

The notation $P(M|B)$ is conditional - probability notation, where the vertical line means "given". So $P(M|B)$ is the probability of event $M$ (selecting a male) occurring given that event $B$ (selecting someone with blue - eyes) has occurred. And $P(B|M)$ is the probability of event $B$ occurring given that event $M$ has occurred. These two conditional probabilities are not the same.

Answer:

What does $P(M|B)$ represent?
A. The probability of getting a male, given that someone with blue eyes has been selected.
Is $P(M|B)$ the same as $P(B|M)$?
A. No, because $P(B|M)$ represents the probability of getting someone with blue eyes, given that a male has been selected.