The probability that a machine is working on any given day is p for some 0 < p < 1, and there are eight of them in a factory.
1. Suppose the factory can operate normally if at least two of the machines work. Find the probability that the factory operates normally for a day.
2. Suppose the factory can operate normally if at least seven of the machines work. Find the probability that the factory operates normally for two days.
p: Probability that machine is working
n = 8
Random variable X: Number of machines working.
X follows Binomial with n = 8 and probability of success p
x = 0,1,2,........n
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