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?
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