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.

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, $P(M|B)=\frac{P(M\cap B)}{P(B)}$ and $P(B|M)=\frac{P(M\cap B)}{P(M)}$, and in general $P(M|B)
eq P(B|M)$ unless $P(M) = P(B)$.

Answer:

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