If the level of infection of a tree is x, 0 ≤ x ≤ 1, then each cure attempt will independently be successful with probability 1 − x. Consider a tree whose infection level, call it L, is assumed to be the value of a uniform (0, 1) random variable.

(a) What is the probability that a single attempt will result in a cure.

(b) Find the probability that the first two cure attempts are unsuccessful.

(c) Find the conditional expected value of L given that it took 3 attempts to cure the tree.