2 Failures of a particular pump being used in a hydroelectri

2. Failures of a particular pump being used in a hydroelectric plant occur randomly, and on average 2 times per year. (a) What is the probability that this pump fails at most 1 time in any Oven 4month period? (8 pts) (b) What is the probability that this pump fails at most 1 time in any given year in fewer than 2 of the next 10 years? (8 pts) (c) What is the probability that this pump will not have failed after being in use for years? (5 pts) (d) Set up (i.e., completely specify) the integral that would enable you to compute the probability of 3 failures occurring for this pump within a 1 year period. (4 pts)

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