A telescope contains 3 large mirrors. The time (in years) untila single mirror fails has been investigated by your colleagues. Younow know that the probability that a mirror is still fullyfunctional after t years is
R(t) = exp −(t/9.4)6
(a) All mirrors must be working to take the most detailedphotographs. What is the proba-
bility that the telescope can produce these types of picturesfor at least 6 years?
(b) The lowest resolution photographs can be taken as long as atleast one mirror is work- ing. What is the probability that thesephotographs can be taken for at least 5 years?
(c) The most common photographs the telescope will be taking areof medium resolution. This is possible as long as at least twomirrors are working. What is the probability that this remainspossible for at least 7 years?
