Question

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

Answer 1

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.