A company is considering a plan that has different profit results under different conditions. Assuming there is a 20% chance of a boom and 10% chance of a recession, compute the expected value of their plan.
Condition Result
Boom $2,000,000 Profit
Average $800,000 Profit
Recession (700,000) Loss
To compute the expected value of the company's plan, we need to multiply the profit/loss for each condition by the corresponding probability and then sum up the results.
Let's break it down step by step:
1. Identify the different conditions and their probabilities:
- Boom: 20% chance
- Average: 70% chance (since the remaining probability is 100% - 20% - 10% = 70%)
- Recession: 10% chance
2. Multiply the profit (or loss) for each condition by its probability:
- For the Boom condition, the profit is $2,000,000 and the probability is 20%, so the contribution to the expected value is: $2,000,000 × 0.20 = $400,000.
- For the Average condition, the profit is $800,000 and the probability is 70%, so the contribution to the expected value is: $800,000 × 0.70 = $560,000.
- For the Recession condition, the loss is ($700,000) and the probability is 10%, so the contribution to the expected value is: ($700,000) × 0.10 = ($70,000).
3. Sum up the results:
The expected value is calculated by summing up the contributions from each condition:
Expected value = $400,000 + $560,000 + ($70,000) = $890,000
Therefore, the expected value of the company's plan is $890,000.