Final answer:
The expected profit after one year for an investment in stock with given probabilities for different outcomes is $150. This is calculated using the expected value formula, taking into account the chances of the stock being worthless, retaining its initial value, or increasing in value.
Step-by-step explanation:
To calculate the expected profit after one year for an investment in stock, we can use the expected value formula, which in this scenario is a weighted average of all possible outcomes.
The given probabilities are: a 35% chance of the stock being worthless, a 60% chance of the stock retaining its value, and a 5% chance of the stock increasing in value by $10,000.
The expected profit E(X) is calculated as follows:
- For the loss of all invested money (stock is worthless): (-$1,000) × 0.35 = -$350
- For no profit and no loss (stock retains value): $0 × 0.60 = $0
- For an increase in stock value by $10,000: $10,000 × 0.05 = $500
The sum of these gives us the expected profit: E(X) = -$350 + $0 + $500 = $150.
Therefore, the expected profit after one year, given the specified probabilities, is $150.