Final answer:
In the context of college-level mathematics, this question regarding investment choices is solved by calculating the expected value for each option. The best option depends on individual risk tolerance, but mathematically, the option with a 5% chance of winning $10,000 has the highest expected value. The correct option is option (4).
Step-by-step explanation:
The subject of this question is Mathematics, specifically dealing with the concepts of probability, expected value, and investment strategies. The grade level is College as the concepts require an advanced understanding of financial mathematics.
To choose between the options, one has to calculate the expected value (EV) for each scenario. The expected value is calculated by multiplying the probability of each outcome by the value of that outcome and summing these products.
Option 1 has a 100% chance of winning $100, so the EV is $100.
Option 2 has a 50% chance of winning $500, so the EV is 0.50 * $500 = $250.
Option 3 has a 25% chance of winning $1,000, so the EV is 0.25 * $1,000 = $250.
Option 4 has a 5% chance of winning $10,000, so the EV is 0.05 * $10,000 = $500.
Considering these calculations, from a purely mathematical standpoint, Option 4 provides the highest expected value. However, individual risk tolerance and financial goals may affect one's investment choice.