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# help

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A machine has 12 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will stop.

Feb 29, 2020

$$\text{The number of components that fail has a binomial distribution, n=12,~p=0.2}\\ P[k>3]=1-P[0]-P[1]-P[2]-P[3] = \\ 1 - \sum \limits_{k=0}^3 \dbinom{12}{k}(0.2)^k(0.8)^{12-k} = 0.205431\\$$