A delivery company uses three depots to distribute packages. Depot X handles 50% of the packages, Depot Y handles 30%, and Depot Z handles 20%.
If a package is handled by Depot X, the probability that it is delivered late is 4%. If a package is handled by Depot Y, the probability that it is delivered late is 5%. If a package is handled by Depot Z, the probability that it is delivered late is 10%.
Draw a tree diagram to represent this information.
A package is selected at random. Find the probability that it is delivered late.
Given that the package is delivered late, find the probability it was handled by Depot Z.
