Question

a pair of dice are rolled and if the sum is a 5, Derek gets a point; if the sum is a 6, Ker gets a point; if the sum is a 7, Gary gets a point. if the sum is some other value, no one gets a point.

(a) if the dice are rolled until Gary gets 4 points, find the probability Derek gets exactly 2 points.

(b) if the dice are rolled until Gary gets 4 points, find the probability that exactly 12 rolls are required.

(c) If the dice are rolled until any one of the players gets a single point, what is the probability the player getting the point is Ker?

(d) what is the expected number of rolls required before the first point is given?

Answer 1