n servers are located in a computer cluster. After one year, each server independently is still working with probability pp, and otherwise fails (with probability 1−p1−p).   What is the probability that at least n−1n−1 servers are working after one year? In your explanaition, provide an answer as an expression in terms of nn and pp. To "Check" your answer, solve the problem with n=12n=12and p=0.89p=0.89. Go with at least three significant digits.

n servers are located in a computer cluster. After one year, each server independently is still working with probability pp, and otherwise fails (with probability 1−p1−p).

What is the probability that at least n−1n−1 servers are working after one year? In your explanaition, provide an answer as an expression in terms of nn and pp. To "Check" your answer, solve the problem with n=12n=12and p=0.89p=0.89. Go with at least three significant digits.