A construction firm purchased 3 tractors from a certain company. At the end of the fifth year, let E1, E2, E3 denote, respectively, the events that tractors no. 1, 2, and 3 are still in good operational condition.
Past experience indicates that the chance of a given tractor manufactured by this company having a useful life longer than 5 years (i.e., in good condition at the end of the 5th year) is 60%. If one tractor needs to be replaced (not in good operational condition) at the end of the 5th year, the probability of replacement for one of the other two tractors is 60%; if two tractors need to be replaced, the probability of replacement of the remaining one is 80%.
a. What is the probability that only tractor no. 1 is in good condition?
b. What is the probability that exactly one tractor is in good condition?
c. What is the probability that at least one tractor is in good condition?