A reliability system consists of 15 independent components. The probability that a component works is 0.9 for each.

The system works if at least 11 of the components work.

Find the probability that the system works.

In another context the 15 probabilities are:

0.9, 0.9, 0.7, 0.8, 0.7, 0.9, 0.7, 0.7, 0.8, 0.8, 0.7, 0.9, 0.8, 0.9, 0.8

Find by simulation, P(system works), the probability that this system works.

Repeat this simulation estimate of P(system works) 200 times. Make a histogram of these estimates, and use this to say something about the uncertainty of the estimate (of P(system works)).