32. Independent trials, each resulting in success with probability p, are performed

(a) Find the expected number of trials needed for there to have been both at least n successes or at least m failures.
Hint: Is it useful to know the result of the first n + m trials?

(b) Find the expected number of trials needed for there to have been either at least n successes or at least m failures.
Hint: Make use of the result from part (a).