The lifetimes of six major components in a copier are

The lifetimes of six major components in a copier are

The lifetimes of six major components in a copier are independent exponential random variables with means of 8000, 10,000, 10,000, 20,000, 20,000, and 25,000 hours, respectively.
(a) What is the probability that the lifetimes of all the components exceed 5000 hours?
(b) What is the probability that at least one component lifetime exceeds 25,000 hours?

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