Find the probability of exactly four successes in five trials of a binomial experiment in which the probability of success is 40%.

Question

Find the probability of exactly four successes in five trials of a binomial experiment in which the probability of success is 40%. Round to the nearest tenth of a percent.

Answer 1

Find the probability of exactly four successes in five trials of a binomial experiment in which the probability of success is 40%. Round to the nearest tenth of a percent.

 

The term of the binomial expansion representing 4 successes in 5 trials is

₅C₄•(0.4)⁴•(0.6).  The factor having exponent 4 represents 4successes; the factor 0.6 represents one failure.

 

The first factor (nCr type) is 5. This factor represents the # of ways in which 4 successes can be distributed in 5 trials.

Calculate this number & adjust decimal point to make % & round as directed.