A venture capitalist

Question

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 9% chance of returning $11,000,000 profit, a 35% chance of returning $2,500,000 profit, and a 56% chance of losing the million dollars. The second company, a hardware company, has a 13% chance of returning $6,000,000 profit, a 36% chance of returning $3,000,000 profit, and a 51% chance of losing the million dollars. The third company, a biotech firm, has a 15% chance of returning $4,000,000 profit, a 45% of no profit or loss, and a 40% chance of losing the million dollars.

Order the expected values from smallest to largest.

Answer 1

Hi Kelly! Expected value = ∑ p_ix_i. That is, for each possible outcome, you take the value of that outcome and multiply by the chance it happens. You then add them all up.

So, for your first opportunity - 3 possible outcome. There is a .09 chance for 11 million, .35 for 2.5 million, and .56 for -1 million (alternatively, 12 million, 3.5 million, and 0 if we're talking about the money left in pocket instead of profit).

So E[X] = .09*11,000,000 + .35*2,000,000 - .56*1,000,000 = 1,130,000.

Try this for the other scenarios!