# 32. Independent trials, each resulting in success with probability p, are performed (a) Find the expected number

## Question:

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).

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