A fair coin is tossed until 100 tails occur Find the probabi

A fair coin is tossed until 100 tails occur. Find the probability that more than 220 coin tosses are required.

There aren\'t any similar examples in my book for this problem, but the chapter is about CLT, Markov/Chebyshev\'s Inequalities. Any help is appreciated.

Solution

You can use technology to solve this problem.

This is a cumulative negative binomial distribution.

In this case, let us consider getting a \"tail\" a \"success\".

Thus, it is asking the probability of getting more than 120 failures before 100 successes.

In that case, we can use technology, such as NEGBINOM.DIST function in Excel. [You can resubmit if you prefer another kind of technology].

As NEGBINOM.DIST gives out the probability for at most f failures, then we need to get the complement of at most 120 failures before 100 successes. Thus,

=1 - NEGBINOM.DIST(120, 100, 0.5, 1)

Which gives

P = 0.078335456 [ANSWER]