Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.
Calculate P(A and O).
Calculate the probability that a package was delivered on time.
If a package was delivered on time, what is the probability that it was service A?
If a package was delivered 40 minutes late, what is the probability that it was service B?
If a package was delivered 40 minutes late, what is the probability that it was service C?