Question: Problem 2.1

Acme Tires manufactures two types of tires: high performance tires and all weather tires. 27% of the tires they produce are high performance tires. They offer a 40,000 mile warrantee on each of the tires they sell, and 93% of all tires exceed 40,000 miles of tread life. Furthermore, 23% of all the tires sold are both all high performance tires AND exceed 40,000 of tread life. You can find this information filled out in the contingency table in tiressp10.xlsx .

(a) Give an example of a simple event.
(b) Give an example of a joint event.
(c) Use the information given to complete the contingency table.
(d) What is the probability that a tire selected at random is an all weather tire?
(e) What is the probability that a tire selected at random fails to last for 40,000 miles?
(f) What is the probability that a tire selected at random is either a high performance tire or fails to last for 40,000 miles?
(g) What is the probability that a tire selected at random is both an all weather tire and exceeds 40,000 miles of tread life?
(h) What is the probability that an all weather tire selected at random exceeds 40,000 miles of tread life?
(i) What is the probability that a high performance tire selected at random exceeds 40,000 miles of tread life?