(a) Many manufacturers of electronic equipment offer a minimum one-year warranty on parts and labour. Retail stores such as 'Courts', 'Singer' and others tend to offer an extended warranty of an additional three (3) years in some instances at an extra cost. You are a customer looking to purchase a refrigerator; based on your knowledge and experience, would you purchase the extended warranty? Say why or why not giving at least one reason support your answer. (8 marks) (b) A warranty is written on a product worth $10,000 so that the buyer is given $8000 if it fails in the first year, $6000 if it fails in the second, $4000 if it fails in the third, $2000 if it fails in the fourth, and zero after that. The probability that the product fails in the first year is 0.1, and the probability that it fails in any subsequent year, provided that it did not fail prior to that year, is 0.1. What is the expected value of the warranty? (12 marks)