Final answer:
The expected value of an original investment of $3000 with a 10% chance of ending up with a value of $2000 is calculated as $200, using the formula for expected value which accounts for the probability and outcomes of the investment.
Step-by-step explanation:
The expected value of an original investment can be calculated by multiplying each possible outcome by its probability and summing all these products. In the scenario presented, there's only one outcome with a non-zero value described, which is a 10% chance of the investment being worth $2000. Thus, the expected value is calculated as follows:
Expected Value = (Probability of Outcome 1 * Value of Outcome 1) + (Probability of Outcome 2 * Value of Outcome 2) + ... + (Probability of Outcome n * Value of Outcome n)
In this case, there's only one outcome to consider:
Expected Value = (0.10 * $2000) + (0.90 * $0)
Expected Value = $200 + $0
Expected Value = $200
Therefore, the expected value of the original investment, given there is only a 10% chance that it'll be worth $2000, is $200.