Question

increase of $25,000 after five years. He can also invest his money in risky assets where there are three outcomes: he has a 31 percent chance of losing $30,000, a 12 percent chance of gaining S15,000 and a 57 percent chance of gaining an unknown amount of money. What must the unknown amount of money equal if the expected value is to equal the guaranteed $25,000? Give your answer to the nearest whole dollar (with no decimal points, spaces, S signs, or commas in your answer)

Is this answer correct? What I calculated is not the same as this answer.

Answer 1

Answer

Expected Value of the gain = P₁V₁ + P₂V₂ + P₃V₃

Here, P₁ = 0.31 + P₂ = 0.12 and P₃ = 0.57

V₁ = Gain with probability P₁ = -30,000 (-ve sign indicates that there is a loss instead of gain)

V₂ = Gain with probability P₂ = 15,000

V₃ = Gain with probability P₃ = X

Hence, P₁V₁ + P₂V₂ + P₃V₃ = 0.31*(-30000) + 0.12*15000 + 0.57*X

We want this equal to 25000

=> 0.31*(-30000) + 0.12*15000 + 0.57*X = 25000

=> 0.57X = 25000 - (0.31*(-30000) + 0.12*15000)

=> X = 57018

Hence, what you have done is absolutely correct.