Discuss why this

As a simple example of how to use random variables, suppose you go to a carnival and contemplate playing playing a game called the Wheel of Cash. The wheel looks like a simple roulette wheel, with three pie-like ie-like wedges. On each wedge is a number: $100, $75. and $5. If the cost to play is $50, should you take a chance on the game? First, note that you have three possible outcomes: $100, 575, and $5. If the wheel is fair-that is, if each outcome has an equal probability of occurring- then the expected value of playing nying the game is (1/3)($100)+(1/3)($75) +(1/3) ($5) - 560. So it looks like a really good de good deal. On average, you'll earn $10 every time you play. But before playing, you should remember this maxim: If a deal seems too good to be true, it probably is. If players could really earn, on average, $10 each time they played, we'd expect to see a very long line of players eager to take their chances. Likewise, we'd expect to see the carnival losing mon ing money on the game. However, because this is an ongoing operation, we sh , we should recognize that it is probably not losing money. What's more likely is that the wheel is not fair and that it lands on the $5 wedge more frequently than on the other two wedges. For example, if the wheel is twice as likely to land o land on the $5 than on the $75 or $100 wedges, then the expected value of playing is only (1/6)($100)+(1/6)($75)+(2/3)($5) = play. $32.50. On average, you lose (and the carnival earns) $17.50 every time you Now, let's return to the decision facing our software development com- pany, XYZ. If the firm decides to develop the complex product (A), it incurs costs of $200K, and then have a 50% chance of launching, and receiving rev- enue of $1 million. If the firm decides to develop the simple product (B), it incurs costs of only $100K, and have a 75% chance of launching, but receiv- ing revenue of $600K. What should XYZ do? We diagram the consequences of the decision in Figure 17.2. XYZ Software Company Develop Product A Develop Product B (0.5) * $80OK + (0.5) * -$200K (0.75) * $50OK + (0.25) * -$100K =$30OK =$350K Launch A Scrap A Launch B Scrap B (probability = 0.5) (probability = 0.5) (probability = 0.75) (probability = 0.25) Firm Profit = $800K Firm Loss = $20oK Firm Profit = $500K Firm Loss = $100K SURE 17.2 Modeling an Uncertain Decision