Express Transit ships products to four different destinations (Warehouse A, Warehouse B, Warehouse C, and Warehouse D). It tracks its shipment by status (Delivered, In-Transit) and and by the shipment's destination.
The shipping data is compiled in the table below.
Required:
Complete the contingency table:
| | A | B | C | D | Total |
|---|---|---|---|---|---|
| Delivered | 20 | 12 | 17 | 21 | 70 |
| In-Transit | 12 | 16 | 53 | 67 | 148 |
| Total | 32 | 28 | 70 | 88 | 218 |
Suppose a tracking number is selected at random. Answer the following questions:
a) What is the probability that the product was delivered? 0.321100917
b) What is the probability that the product is for Warehouse C? 0.321100917
c) What is the probability that the product was for Warehouse D and Delivered? 0.096330275
d) What is the probability that the product was not for Warehouse A? 0.853211009
e) Suppose the product selected was for Warehouse B. What is the probability that the product was delivered? 0.428571429
f) What is the probability that a Delivered product was for Warehouse D? 0.3
g) What is the probability that the product was Delivered or was for Warehouse D?