Amachine relies on the functioning of 3 parts, each of which functions correctly with probability p and does not function with probability (1-p). all three parts function independently of the others, and the machine only works if at least 2 of the 3 parts are operating.
a. compute the probability that the machine is functioning
b. suppose that the value of the probability becomes random. assume that p is a uniform random variable taking real values between 0 and 1, independent of the state of the system, and that all three parts share the same random variable p.
what is the probability that the machine is functioning in this random environment?