Excel
Excel has a function that will evaluate either single negative binomial probabilities or cumulative probabilities, "NEGBINOM.DIST()". For example, if the probability of success is π = 0.3 and we are interested in how long it takes to get \(k = 5\) successes,
Excel is implicitly using the second form of binomial distribution for the number of failures before the \(k\)'th success.
On a scientific calculator
Negative binomial probabilities can also be found on a scientific calculator directly using the formula for its probability function.
Question
If a coin is repeatedly tossed, what is the probability that the second head will appear on the fifth toss of the coin?
(Solved in full version)