binomial distribution

Question

Find the probability of at least one failure in five trials of a binomial experiment in which the probability of success is 30%. Round to the nearest tenth of a percent.

Answer 1

If you think about it, you will realize that there are only 6 possible outcomes for the number of failures in five trials of a binomial experiment. You can have 0, 1, 2, 3, 4, or 5 failures. Only 1 of these outcomes (0 failures) does not have at least one failure. So just find the probability of 0 failures (which is the same thing as having 5 successes) and subtract this number from 1.