Consider the purchasing patterns shown in the table below, involving different computer components. Which of the components does the consumer actually end up buying most frequently in the long run?

	Component 1	Component 2	Component 3
Component 1	30%	30%	40%
Component 2	30%	45%	25%
Component 3	50%	40%	10%

b) Find the probability that the consumer purchases Component 1first, tries it again or some other product, and then purchases Component 1 the next time.

c) Create the transition matrix C using the chart showing the purchases, find C², and find the probability that a consumer starting with Component 1 would return to it in two more purchases. Compare and discuss in details your solutions for question b) and c).

d) Find C3, C4, C5 and C6, each with 6 decimal places. Write down the probabilities of buying a particular component at the fifth purchase time after the initial purchase with 3 decimal places. Discuss in details your observations.

e) Which component will the consumer buy? Explain in details your conclusions.