The property restoration company PuroServ is considering switching to new dehumidifiers. Their market research, considering the cost of the new machines and their efficiency, tells them that the switch would give them a 54% chance of making a $20,000 profit, a 23% chance of breaking even, and a 23% chance of losing $5,000. How much money does PuroServ expect to make with their new purchase?
Not sure what to do with this one....
To determine how much money PuroServ expects to make with their new purchase, we need to calculate the expected value. The expected value is the average value of the profits weighted by their respective probabilities.
First, we need to calculate the profit for each outcome:
- Making a $20,000 profit with a 54% chance: $20,000 * 0.54 = $10,8000.
- Breaking even with a 23% chance: $0 * 0.23 = $0.
- Losing $5,000 with a 23% chance: -$5,000 * 0.23 = -$1,150.
Now, we can calculate the expected value by summing up the weighted profits:
Expected Value = (Probability of Outcome 1 * Profit of Outcome 1) + (Probability of Outcome 2 * Profit of Outcome 2) + (Probability of Outcome 3 * Profit of Outcome 3)
Expected Value = (0.54 * $10,800) + (0.23 * $0) + (0.23 * -$1,150)
Expected Value = $5,832 + $0 - $264.5
Expected Value = $5,567.5
Therefore, PuroServ expects to make $5,567.5 with their new purchase.