A videocassette recorder manufacturer is so certain of its quality control that it is offering a complete replacement warranty if a recorder fails within 2 years. Based upon compiled data, the company has noted that only 3.0 percent of its recorders fail during the first year, whereas 2.0 percent of the recorders that survive the first year will fail during the second year. The warranty does not cover replacement recorders.
a. Formulate the evolution of the status of a recorder as a Markov chain whose states include two absorption states that involve needing to honor the warranty or having the recorder survive the warranty period. Then construct the (one-step) transition matrix.
b. Find the probability that the manufacturer will have to honor the warranty.