Acme Tires manufactures two kinds of tires: high performance tires and all weather tires. 37% of tires they produce are high performance tires. They offer a 40,000 mile warrantee on each of the tires they sell, and 96% of all tires exceed 40,000 miles of tread life.
Furthermore, 34% of all tires sold are both all high performance tires AND exceed 40,000 of tread life.
Employ probability theory to answer the following questions:
(a) Provide an example (related to the setting of the question) of a simple event.
(b) Provide an example (related to the setting of the question) of a joint event.
(c) Employ the information given to complete the contingency table.
(d) Determine the probability that a tire selected at random is an all weather tire?
(e) Determine the probability that a tire selected at random fails to last for 40,000 miles?
(f) Determine the probability that a tire selected at random is either a high performance tire or fails to last for 40,000 miles?
(g) Find out the probability that a tire selected at random is both an all weather tire and exceeds 40,000 miles of tread life?
(h) Find out the probability that an all weather tire selected at random exceeds 40,000 miles of tread life?
(i) Find out the probability that a high performance tire selected at random exceeds 40,000 miles of tread life?