Question

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.

Answer #1

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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