An investment company has produced the following table, which shows the probabilities of various percentage profits on money invested over a period of 3 years.

a. Calculate the expected profit on an investment of $50000.

b. A woman considers investing $50000 with the company, but decides that her money is likely to earn more when invested over the same period in a savings account that pays r% compound interest per annum.

Calculate, correct to 2 decimal places, the least possible value of r.

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Profit 1 5 10 15 20 30 Can 40 45 50 Prooility 0.05 0.10 0.50 0.20 0.05 0.04 0.03 0.02 0.01