Question: 4.2. Suppose that three components in a certain system each function with probability p and fail with probability 1 - p, each component operating or

4.2. Suppose that three components in a certain system each function with probability p and fail with probability 1 - p, each component 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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