To solve this problem, let's consider the possible outcomes and their respective probabilities. We'll calculate the expected value for the investment, which represents the average amount of money an investor can expect to have after making such investment multiple times.
We start with the following information:
- Initial investment: \[tex]$2000
- A 20% chance to double the money (i.e., get \$[/tex]4000)
- A 30% chance to break even (i.e., end up with the initial \[tex]$2000)
- A 35% chance to lose \$[/tex]1000 (ending up with \[tex]$1000)
- A 15% chance to lose the entire investment (ending up with \$[/tex]0)
Step-by-Step Calculation:
1. Determine the outcomes:
- If the investment doubles, the outcome is \[tex]$4000.
- If the investment breaks even, the outcome is \$[/tex]2000.
- If the investment loses \[tex]$1000, the outcome is \$[/tex]1000.
- If the investment loses the entire amount, the outcome is \[tex]$0.
2. Assign probabilities to each outcome:
- Probability of doubling: 0.20
- Probability of breaking even: 0.30
- Probability of losing \$[/tex]1000: 0.35
- Probability of losing all: 0.15
3. Calculate the expected value (EV):
The expected value is obtained by multiplying each outcome by its probability and then summing these products.
[tex]\[
EV = (0.20 \times 4000) + (0.30 \times 2000) + (0.35 \times 1000) + (0.15 \times 0)
\][/tex]
4. Perform the calculations:
- For doubling the money: [tex]\(0.20 \times 4000 = 800\)[/tex]
- For breaking even: [tex]\(0.30 \times 2000 = 600\)[/tex]
- For losing \[tex]$1000: \(0.35 \times 1000 = 350\)
- For losing all: \(0.15 \times 0 = 0\)
Summing these values gives:
\[
EV = 800 + 600 + 350 + 0 = 1750
\]
Thus, the expected value of the investment is \$[/tex]1750.
5. Determine the net gain or loss:
To find the net gain or loss, we subtract the initial investment from the expected value.
[tex]\[
\text{Net Gain/Loss} = EV - \text{Initial Investment}
\][/tex]
Given:
- EV = \[tex]$1750
- Initial Investment = \$[/tex]2000
[tex]\[
\text{Net Gain/Loss} = 1750 - 2000 = -250
\][/tex]
So, the expected value of this investment is \[tex]$1750, and the expected net loss is \$[/tex]250.
Conclusion:
The expected net loss of \[tex]$250 suggests that, on average, an investor can expect to lose \$[/tex]250 per investment of \$2000. This indicates that such an investment strategy is not generally advisable for long-term investment, as it tends to yield a negative return. However, individual decisions may vary based on the investor’s risk tolerance and overall investment strategy.
