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 each profit or loss outcome by its corresponding probability and then sum up the results.

Let's start by calculating the expected value for each condition:

Boom: Profit of $2,000,000 with a 20% chance:
Expected value = $2,000,000 * 0.20 = $400,000

Average: Profit of $800,000 with a 70% chance (100% - 20% - 10%):
Expected value = $800,000 * 0.70 = $560,000

Recession: Loss of $700,000 with a 10% chance:
Expected value = -$700,000 * 0.10 = -$70,000 (note the negative sign)

Now, we can sum up the expected values of each condition to get the overall expected value of the company's plan:

Expected value = $400,000 + $560,000 - $70,000 = $890,000

Therefore, the expected value of the company's plan is $890,000.