A company is considering the expansion of its current facility to meet increasing demand. A major expansion would cost $500,000, while a minor expansion would cost $200,000. If demand is high in the future, the major expansion would result in an additional profit of $800,000, but if demand is low, then there would be a loss of $500,000. If demand is high, the minor expansion will result in an increase in profits of $200,000, but if demand is low, then there is a loss of $100,000. The company has the option of not expanding. For what probability of a high demand will the company be indifferent between the two expansion alternatives?

Let's denote the probability of high demand as P.

For the major expansion:

If demand is high, additional profit = $800,000

If demand is low, loss = -$500,000

The expected value (EV) of the major expansion = P x 80,000 + (1 - P) x (-50,000)

For the minor expansion:

If demand is high, additional profit = $200,000

If demand is low, loss = -$100,000 

The expected value (EV) of the major expansion = P x 2,00,000 + (1 - P) x (-1,00,000)

The company is indifferent between the two options when the expected values are equal:

P × 800,000 + (1 - P) x (-50,000) = P x 2,00,000 + (1 - P) x (-1,00,000)

Let's solve for P:

800,000 P − 500,000 + 500,000 P = 200,000 P − 100,000 + 100,000

800,000 P + 500,000 P = 200,000 P+100,000

1,300,000 P = 200,000 P + 100,000

1,100,000 P =100,000

P = 1,00,000 / 11,00,000

P = 0.0909

Therefore, the company would be indifferent between the major and minor expansions if the probability of high demand is approximately 0.0909, or roughly 9.09%.