To determine the best investment option, we should compare the expected return of each option. The expected return (ER) is calculated by multiplying each possible return by its probability and then summing these values.

a. Option A: Return 0 with 0.45 probability or 20k with 0.55 probability

The expected return is calculated as: $ER_A = (0 \times 0.45) + (20,000 \times 0.55)$ $ER_A = 0 + 11,000 = 11,000$

b. Option B: Return 10k with 0.5 probability or 12k with 0.5 probability

The expected return is calculated as: $ER_B = (10,000 \times 0.5) + (12,000 \times 0.5)$ $ER_B = 5,000 + 6,000 = 11,000$

c. Option C: Return 11k with 1 probability

The expected return is: $ER_C = 11,000$

Conclusion:

• ER_A = 11,000
• ER_B = 11,000
• ER_C = 11,000

All three options have the same expected return of 11,000. However, risk tolerance will likely influence the decision:

• Option A has higher variability (risky, with a chance of losing everything).
• Option B has moderate variability but no chance of loss.
• Option C is risk-free with a guaranteed return of 11k.

The best choice depends on the investor's risk appetite. If the investor prefers certainty, Option C is the best. If they are willing to take a risk for potentially higher returns, Option A may be considered.

Would you like to explore more detailed risk analysis or decision-making criteria?

Relative questions:

1. How does an investor's risk tolerance affect their choice in this scenario?
2. What is the concept of expected return in investment decision-making?
3. How does variance in returns influence an investor's decision?
4. What other factors, aside from expected return, should be considered when investing?
5. How can diversification help in managing investment risk?

Tip:

Always compare not just expected returns but also the risk involved, which can be measured using variance or standard deviation of the outcomes.