telescope contains 3 large mirrors. The time (in years) until a single mirror fa

Question

telescope contains 3 large mirrors. The time (in years) until a single mirror fails
has been investigated and we know that the probability that a mirror is still fully
functional after t years is e-(t/10)5
.
(a) All mirrors must be working to take the most detailed photographs. What is
the probability that the telescope can produce these types of pictures for at
least 5 years?
(b) The lowest resolution photographs can be taken as long as at least one mirror
is working. What is the probability that these photographs can be taken for
at least 7 years?
(c) The most common photographs the telescope will be taking are of medium
resolution. This is possible as long as at least two mirrors are working. What
is the probability that this remains possible for at least 6 years?

Explanation / Answer

P = e-(t/10)^5 a) required probability = [e-(5/10)^5]3 = 0.91 b)required probability = e-(7/10)^5 = 0.845 c)required probability = [e-(6/10)^5]^2 = 0.925

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