A workshop has several machines. During a typical month, two machines will break down. The probability of more than two machines will break down in a month is

Poisson's Distribution:

P (X = r) = \({e^{-λ} \space λ^r\over r!}\)

where, λ = Mean or average value

Calculation:

The probability of more than two machines will breakdown in a month is:

P(X > 2) = 1 – P(X ≤ 2)

P(X > 2) = 1 – \(({e^{-λ} \space λ^0\over 0!}+{e^{-λ} \space λ^1\over 1!}+{e^{-λ} \space λ^2\over2!})\)

Given, λ = 2

P(X > 2) = 1 – \(({e^{-2} \space 2^0\over 0!}+{e^{-2} \space 2^1\over 1!}+{e^{-2} \space 2^2\over2!})\)

P(X > 2) = 1 - 5e-2