Acme Tires manufactures two types of tires: high performance tires and all weath

Question

Acme Tires manufactures two types of tires: high performance tires and all weather tires. 37% of the 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 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 the Data tab. Use this information to answer the following questions. Questions 2.1 and 2.2 relate to information from week 4 in the class, 2.3 comes from week 5 material, and 2.4 is based on material from week 6. Note that part a (and ONLY part a) of question 2.3 is an extra credit question. Should you encounter any difficulties with these problems, the optional problems below are very similar to the questions in this problem set, and the answers to the optional questions can be found in the back of the textbook. You can also request that the tutor work extensively with you on the optional problems.

1

Use probability theory to answer the following questions:

(a) Give an example (related to the setting of the question) of a simple event.
(b) Give an example (related to the setting of the question) of a joint event.
(c) Use the information given to complete a joint probability 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?

3

Use probability theory to answer the following questions:

(a) Give an example (related to the setting of the question) of a simple event.
(b) Give an example (related to the setting of the question) of a joint event.
(c) Use the information given to complete a joint probability 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?

Explanation / Answer

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