Question

A certain company sends 50% of its overnight mail parcels via express mail service E1. Of these parcels, 1% arrive after the guaranteed delivery time (denote the event late delivery by L). Suppose that 10% of the overnight parcels are sent via express mail service E2 and the remaining 40% are sent via E3. Of those sent via E2 only 2% arrive late, whereas 5% of the parcels handled by E3 arrive late. Part a: Draw a tree diagram for this problem.

Answer 1

The probability that a person must wait at least 1.5 more hours is 0.4.

Step-by-step explanation:

A tree diagram is a graphical representation that displays the hierarchical structure of a set of interconnected elements. It is often used to depict the outcomes of a series of events or decisions in a systematic way. Tree diagrams are particularly useful in probability theory, decision analysis, and problem-solving to visualize different paths and outcomes.

Tree Diagram

Here is a tree diagram for the given problem:

Answer to part a:

The probability that a person must wait at least 1.5 more hours is 0.4. This means that there is a 40% chance that a person will have to wait for 1.5 or more hours past noon on a delivery day.