The Megabuck Computer Company is thinking of introducing two new products. The first, Model 101, is a small computer designed specifically for children between ages 8 and 16. The second, Model 202, is a medium-size computer suitable for managers. Because of limited production capacity, Megabuck has decided to produce only one of the products. The profitability of each model depends on the proportion of the potential market that would actually buy the computer. For Model 101, the size of the market is estimated at 10 million, whereas for Model 202, the estimate is 3 million.
After careful analysis, the management of Megabuck has concluded that the percentage of buyers of Model 101 is 5%, 10%, or 15%. The respective profits are given here.
Percent Who Buy Model 101................................ Net Profits ($ Millions)
5................................................................................................ 20
10................................................................................................ 100
15................................................................................................ 210
An expert in probability from the local university estimated the probability of the percentages as P(5%) = .2, P(10%) = .4, and P(15%) = .4. A similar analysis for Model 202 produced the following table.

Percent Who Buy Model 202.................................. Net Profits ($ Millions)
30...................................................................................................... 70
40...................................................................................................... 100
50...................................................................................................... 150

For this model, the expert estimated the probabilities as P(30%) = .1, P(40%) = .4, and P(50%) = .5.
a. Based on this information, and with the objective of maximizing expected profit, which model should Megabuck produce?
b. To make a better decision, Megabuck sampled 10 potential buyers of Model 101 and 20 potential buyers of Model 202. Only 1 of the 10 wished to purchase the Model 101, whereas 9 of the 20 indicated that they would buy Model 202. Given this information, revise the prior probabilities and determine which model should be produced.