# Math Help - Probability Question

1. ## Probability Question

You are evaluating 2 systems for a company. System 1 has 4 valves in sequence. If one fails, the system fails. The probability a value will fail is .01(1%)(assume independence)

What is the probability system 1 will not fail?

System 2 has 3 values. The probability a valve will fail is .4(40%)(assume independence).BUT in system 2, as long as one of the values does not fail, the system will not fail.

What is the probability that system 2 will not fail?
What is the probability that system 2 will fail?

I tried using various numbers using the Bayes Theorem and tried to put actual numbers, but could not the right answer.

Thanks,
Shawn

2. In system 2 assume that the valves are A, B, & C.
It does not fail: $1-P(A^cB^cC^c)=1-(0.4)^3$.

3. according to your equation I get 0.784, but the answer in my answer sheet states .936. Something no right

$1-(0.4)^3$