Suppose that breakdowns of a machine occur randomly, according to a poisson proc

Question

Suppose that breakdowns of a machine occur randomly, according to a poisson process having a rate of 1 breakdown per week (7 days). What is the probability that no breakdowns occur on at least 6 of the next 7 days?

Note: this problem consists of two parts. The first is finding the poisson process for a single day, and the second is using a distribution (binomial?) to calculate the probability of no breakdowns on "at least 6 of the next 7 days". This problem is not asking for the poisson distribution of P(X>=6).

Explanation / Answer

By using Poisson distribution

P(x = 0) = e-1 * 1^0/0! = 0.368

By using binomial distribution

P(x >6) = P(X = 6) + P(X = 7)

= 7C6 * (0.368)^6 * (0.632)^1 + 7C7 * (0.368)^7 * (0.632)^0 = 0.012

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