You are considering two investment opportunities. For investment A there is a 25% chance that you lose $20,000, a 50% chance that you break even, and a 25% chance that you make $80,000. For investment B there is a 30% chance that you lose $50,000, a 50% chance that you break even, and a 20% chance that you make $180,000. Based on the expected value of each, which investment should you make?
Answer:
you should make investment B
Step-by-step explanation:
The expected value of a discrete variable is calculated as:
\(E(x)=x_1P(x_1)+x_2P(x_2)+ ... + x_nP(x_n)\)
Where \(x_1, x_2, ... x_n\) are the possible values for the variable and \(P(x_1), P(x_2), ... P(x_n)\) are their respective probabilities.
Then, the expected value for investment A is:
E(A) = -20,000(0.25) + 0(0.5) + 80,000(0.25) = $15,000
Because, you can lose $20,000 with a probability of 0.25, you can break even with a probability of 0.5 or you can win $80,000 with a probability of 0.25.
At the same way, the expected value for investment B is:
E(B) = -50,000(0.3) + 0(0.5) + 180,000(0.2) = $21,000
Then, you should make investment B because the expected value for investment B is bigger than the expected value for investment A.