Problem 4 (9 pts)
For an experiment consisting of a sequence of independent trials, the probability of success of each trial is $p$.
(a) (3 pts) If the probability of observing 3 failures before 2 successes is 0.1345662, verify that $p = 0.35$.
(b) (3 pts) If there are 10 trials and $p = 0.4$, and let $X = $ number of successes, what is $V(X)$?
(c) (3 pts) If $p = 0.9$, and we repeat the trials until we observe a success, what is the probability that we
observed less than 3 failures?