Three messenger services deliver to a small town in Oregon. ServiceAhas 60% of all the scheduled deliveries, serviceBhas 30%, and serviceChas the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively.

b. A package arrived on time.What is the probability it was delivered by service B?

c. A package arrived on time.What is the probability it was delivered by service A?

d. You give your package to service C.What is the probability it'll be delivered late?

I think this is similar to a binomial probability distribution problem.

If that is the case, could I use p^x*(1-p)^n-x?