Question

Customers buy cell phones from three companies. Given the company from which a customer last bought a phone, the probability that she will buy her next phone from each company is as follows:

	Will Buy Next From
Last Bought From	Company 1	Company 2	Company 3
Company 1	0.80	0.10	0.10
Company 2	0.05	0.85	0.10
Company 3	0.10	0.20	0.70

A. If someone currently owns a company 1 phone, what is the probability that at least one of the next two phones she buys will be a company 1 phone?

B. At present, it costs company 1 an average of $500 to produce a phone, and the average price a customer pays for one is $800. Company 1 is considering instituting a two-year warranty. It estimates that this will increase the cost per phone by $30, but a market research survey indicates that the probabilities will change as follows:

	Will Buy Next From
Last Bought From	Company 1	Company 2	Company 3
Company 1	0.85	0.10	0.05
Company 2	0.10	0.80	0.10
Company 3	0.15	0.10	0.75

Should company 1 institute the warranty program?

Answer 1

A. If someone currently owns a company 1 phone, what is the probability that at least one of the next two phones she buys will be a company 1 phone

P(not from company 1 ) =1-0.8 = 0.2

Let A be the last 2 phone from other than 2 company

P(A) = 0.2 * 0.2 = 0.04

= 1- 0.04 = 0.96

2)

Expected Cost =0.80 * 300 =240

Expected Cost =0.85 * 270=229.5

Company 1 ishould not nstitute the warranty program as expected profit was better before.

Please revert back in case of any doubt.

Please upvote. Thanks in advance.