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

Out of 5 trials, "at least one failure" = " at most four successess", so the probability you're looking for is

`P(X\le 4) = \displaystyle\sum_(x=0)^4 \binom5x 0.30^x (1-0.30)^(5-x) \approx 0.99757 \approx \boxed{99.8\%}`