We roll a fair die four times.

(a) describe the sample space ohm and the probability measure p that models this experiment (i. e., give the value p(omega) for each outcome omega elementof ohm).

(b) let a be the event that there are at least two fives among the four rolls. let b be the event that there is at most one five among the four rolls. find the probabilities p(a) and p(b), by finding the ratio of the number of favorable outcomes to the total, as in the equally likely outcomes rule.

(c) what is the set aub? what equality should p(a) and p(b) satisfy? check that your answers to part (b) satisfy this equality.