Three children take turns shooting a ball at a basket. They each shoot until they misses and then it is next child’s turn. Suppose that child i makes a basket with probability pi and that successive trials are independent.

(a) Determine the proportion of time in the long run that each child shoots.

(b) Find the answer when p1 D 2=3; p2 D 3=4; p3 D 4=5.