Choose an employee person at random. let a be the event that the person is a female and b be the event that the person holds a managerial position. data from the us department of labor suggests that p(a)= 0.47 and p(b|a)= 0.34.

perform the following:

a) explain what p(a)= 0.47 means in context
b) explain what p(b|a)= 0.34 means in context
c) what is the probability that a randomly chosen employed person is a male?
d) what is the probability that a randomly chosen employed person is a female manager?
e) what is the probability that a randomly chosen employed female is not a manager?

Problems and applications q5 four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. here is their willingness to pay for each film: willingness to pay (dollars) shen antonio dmitri jake first film 10 9 8 3 second film 8 7 6 2 third film 6 5 4 1 fourth film 4 3 2 0 fifth film 2 1 0 0 within the dorm room, the showing of a movie a public good. if it costs $12 to rent a movie, the roommates should rent movies in order to maximize the total surplus. suppose the roommates choose to rent the optimal number of movies you just indicated and then split the cost of renting equally. this means that each roommate will pay $ .