An aircraft is required to complete a sequence of missions A

An aircraft is required to complete a sequence of missions. After each mission, maintenance is performed on the aircraft for 30 minutes. This maintenance practice results in 60% of missions being performed with the aircraft in good condition, 30% of missions in fair condition, and 10% of missions in poor conditions. If the aircraft is in good condition, then the mission requires 45 minutes to complete and the probability of mission success is 0.95. If the aircraft is in fair condition, then the mission requires 60 minutes to complete and the probability of mission success is 0.75. If the aircraft is in poor condition, then the mission requires 90 minutes to complete and the probability of mission success is 0.6. What is the probability of mission success? Given that the mission was successful, what is the probability that the aircraft was in good condition? On average (expected value), how long does it take to complete a mission?

Solution

Answer: ( 0.6*45 + 0.3*60 + 0.1*90) + 30 = 84 minutes (The probability of the mission success has nothing to do with the question asked)