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

Explanation:

The notation $P(A|B)$ represents the conditional - probability of event $A$ occurring given that event $B$ has occurred. So, $P(M|B)$ is the probability of getting a male given that someone with blue eyes has been selected. And $P(B|M)$ is the probability of getting someone with blue eyes given that a male has been selected. These two conditional probabilities are not the same.

Answer:

What does $P(M|B)$ represent?
B. The probability of getting a male, given that someone with blue eyes has been selected

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