10,000 investment. 3/9 chance of returning 18,000, 6/9 chance of losing all the money. What is the expected value?

The expected value (EV) is a calculation that represents the average outcome of a probabilistic event. In your case, you are investing $10,000 with two possible outcomes:

- **Return $18,000** with a probability of $ \frac{3}{9} $
- **Lose all your money** with a probability of $ \frac{6}{9} $

Here’s how to compute the expected value:

\[
EV = ( \text{probability of gain} \times \text{gain amount} ) + ( \text{probability of loss} \times \text{loss amount} )
\]

Let's calculate it:

\[
EV = \left(\frac{3}{9} \times 18,000\right) + \left(\frac{6}{9} \times 0\right)
\]

\[
EV = \left(\frac{1}{3} \times 18,000\right) + \left(\frac{2}{3} \times 0\right)
\]

\[
EV = 6,000 + 0 = 6,000
\]

So, the expected value of your investment is **$6,000**.

This means that, on average, over many similar investments, you would expect to end up with $6,000.

Would you like more details on expected value calculations or other questions about risk and probability?

Here are some related questions:
1. How does expected value influence decision-making in finance?
2. What is the risk-neutral approach to investments?
3. How does variance relate to expected value in financial decisions?
4. What is the probability of a breakeven point in this scenario?
5. How would you account for additional factors like inflation or fees?

**Tip:** Always consider not just the expected value but also the risk (probability distribution) when making investment decisions!

Calculate the expected value of a $10,000 investment with a 3/9 chance of returning $18,000 and a 6/9 chance of losing all the money. Learn about probability and expected value, with step-by-step guidance for students in Grades 9-12.

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