If the Acme Company makes a profit in any given year, the probability that it will make a profit the following year is 0.9. On the other hand, if it makes a loss in any given year, the probability of a loss in the following year is 0.5. In year 1, the company made a profit. Use a decision tree diagram to illustrate Acme’s profit and loss situations for the next three years, i.e., up to year 4.

What is the probability that Acme made a loss in year 4? If it is known that Acme made a profit in year 2, what is the probability that it made a profit in year 4?

(Answers: (i) probability of a loss in year 4 is 0.156 (ii) probability of a profit in year 4 is 0.86.)