1. The problem statement, all variables and given/known data A 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 probabilty that the telescope ca 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? 2. Relevant equations 3. The attempt at a solution a) e^(-(4/10)^5 ) = 0.9898122503 0.9898122503 × 1/3 = 0.3299374168 P(X ≥ 5) = (1 - 0.3299374168) = 0.6700625832 Probability that all mirrors are functional for at least 5 years is 67% b) e^(-(6/10)^5 ) = 0.9251864446 P(X ≥ 7) = (1 – 0.9251864446) = 0.07481355535 Probability that at least one mirror is functional for at least 7 years is 7% c) e^(-(5/10)^5 ) = 0.9692332345 0.9692332345× 2/3 = 0.6461554897 P(X ≥ 6) = (1 – 0.6461554897) = 0.3538445103 Probability that at least 2 mirrors is functional for at least 6 years is 35% I'm not too sure if this is the right working, could someone please verify this for me?