This question involves choosing between a stock and a bond investment, with given probabilities and returns.

Step-by-step breakdown:

1. Stock investment:

   • The stock has a 30% chance to rise to $2,200 and a 70% chance of becoming worthless.
   • Expected return from stock: $E[\text{Stock}] = (0.30 \times 2200) + (0.70 \times 0) = 660 + 0 = 660$ The expected wealth from the stock is $660.

2. Bond investment:

   • The bond promises a certain return of 25%. If you invest $1,000 in the bond, you will get: $\text{Bond Return} = 1000 \times (1 + 0.25) = 1250$ The bond guarantees $1,250 at the end of the year.

3. Decision:

   • Comparing the expected return from the stock ($660) with the bond's guaranteed return ($1,250), the bond is the safer and more profitable choice based on expected value.

4. How much wealth is reduced by making the wrong choice:

   • If you choose the stock over the bond, the reduction in expected end-of-year wealth is: $\text{Wealth Reduction} = 1250 - 660 = 590$ So, your expected wealth would be reduced by $590 if you choose the stock instead of the bond.

Would you like more details or have any questions?

Follow-up questions:

1. What would be the expected return if the probability of stock success were higher?
2. How does risk aversion factor into this investment decision?
3. What is the variance of the expected returns for the stock?
4. How could the time horizon affect the choice between stock and bond?
5. If the bond offered a lower return, at what rate would the stock become the better choice?

Tip: Always compare both the expected returns and the risks involved when making investment decisions.