A small retail store sells a particular brand of monochrome and color television sets. Each monochrome set that is sold earns a profit of $100, while each color set earns $200 profit. The manager of the store estimates that the weekly demands for each type of set follow the probability distributions shown below. It can be assumed that the demands for each type of set are independent, as is the week-to-week demand.
Demand per week Monochrome sets Color sets
0 0.2 0.4
1 0.5 0.6
2 0.3
(a) Determine the possible total profits that can be earned in any given week by selling television sets and calculate the probability of each of these profits being earned.
(b) The following two-digit random numbers have been generated by a computer. Use these numbers to simulate the demand for the two types of set for a 10-week period and hence calculate the profit that will be earned in each week. (The first set of numbers should be used for monochrome sets and the second for color.)
Monochrome
71 82 19 50 67 29 95 48 84 32
Color
36 44 64 92 39 21 18 55 77 73
(c) Use your simulation results to estimate the probability of particular profits being earned in a given week. How close are these probabilities to those that you calculated in (a)?