Question

1. Archway Adventures has compiled data for 2017 on customer orders by region and product group as follows:

	North America	Europe	Rest of World	Total
Children’s Toys	5,400	2,700	900	9,000
Games	4,200	2,700	1,100	8,000
Other	1,300	900	800	3,000
Total	10,900	6,300	2,800	20,000

Let us assume that these are representative of the pattern of orders that they anticipate seeing in 2018.

1. What is the probability that a randomly selected order will be from North America?
2. What is the probability that an order is from North America and it is for a game?
3. What is the probability that an order is from outside North America and Europe or is for something other than a toy or game?
4. Among orders from the “rest of the World”, what is the probability it is for a toy?
5. Among orders for toys, what is the probability that the order comes from the “Rest of the World”?
6. Are the events “Toy” and “Rest of the World” independent? Explain.
7. The rows of the table are mutually exclusive categories. How would our summary be complicated if some orders were for multiple products?

2. 54.5% of Archway’s orders come from North America, 31.5% from Europe and the remaining 14% from the rest of the world. Among North American customers, 3% complained about late or lost deliveries. Similarly, complaints were received from 8% of European customers and 15% of customers from the rest of the world.

1. Construct a probability tree that shows all combinations of where orders originated and whether customers complained. Label all branches in terms of what the event is on the branch and the corresponding probability (e.g., P(A), PA’), P(B|A), P(B’|A),…). Also determine the probability for each ending joint event (e.g., P(Europe and Complain)).
2. Summarize all of the joint probabilities in a probability table.
3. What percentage of Archway customers complained about delivery problems?
4. Among those who complained, what percentage were from Europe?

Answer 1