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.
The number of components that fail has a binomial distribution, n=12, p=0.2P[k>3]=1−P[0]−P[1]−P[2]−P[3]=1−3∑k=0(12k)(0.2)k(0.8)12−k=0.205431
