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 a male or getting someone with blue eyes. d. the probability of getting someone with blue eyes, given that a male has been selected.

Explanation:

In probability, the notation $P(A|B)$ represents the conditional - probability of event $A$ occurring given that event $B$ has already occurred. Here, $M$ is the event of selecting a male and $B$ is the event of selecting someone with blue eyes. So, $P(M|B)$ is the probability of getting a male given that someone with blue eyes has been selected. Also, $P(B|M)$ is the probability of getting someone with blue eyes given that a male has been selected. These two conditional probabilities are not the same in general as they have different conditions.

Answer:

A. The probability of getting a male, given that someone with blue eyes has been selected.
No, $P(M|B)$ is not the same as $P(B|M)$.