Question: Suppose that three components in a certain system each function with probability p and fail with probability 1-p , each components operating or failing independently

Suppose that three components in a certain system each function with probability p and fail with probability 1-p , each components operating or failing independently of the others. But the system is in a random environment so that p is itself a random variable. Suppose that p is uniformly distributed over the interval (0,1]. The system operates if at least two of the components operate. What is the probability that the system operates ?

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