The probability of an engine's failing during a 30 day acceptance test is 0.3 under adverse environmental conditions. Eight engines are included in such a test. What is the probability of the following?

a) None will fail

b) All will fail

This is an example of binomial probability (pass/fail), with n=8 and p (failure) = 0.3.

The probability that none will fail is binompdf (8,0.3,0) = 0.0576.

The prob. that all will fail is found by subtracting this result from 1.0000, and is 1.0000-0.0576=0.9424. "All" is the "complement" of "None."

I used my TI-83 Plus calculator's probability distribution functions to calculate the probability that none will fail.