Let X be the number of successes in 7 independent trials of a binomial experiment in which the probability of success is p = . Find the following probabilities. (Round your answers to four decimal places.)
(a) P(X = 6).

If the probability of sucecss for any one trial is p, that means the probability of a failure is (1-p). So to get 6 successes followed by one failure the probability is . But the one failure does not have to be the last trial - it could be any one of the 7 trials. Hence you multiply this by 7.

Mathematically the formula for determining the probability of getting k successes in n trials is

Mathway.com ! (: