Question

You want to invest $1000. There is a 10% chance you lose all of the investment, a 20% chance

you lose $200, a 20% chance you break even, a 20% chance you make $200, and a 30% chance
you make it big and end up with $2000. What is the expected value?

Answer 1

The expected value of the investment is -$193.

Step-by-step explanation:

The expected value of an investment is calculated by multiplying each possible outcome by the probability of that outcome, and then summing up the results. In this case, let's assign the following values to the outcomes: losing all of the investment (-$1000), losing $200 (-$200), breaking even ($0), making $200 (+$200), and making $2000 (+$2000). The probabilities are 10%, 20%, 20%, 20%, and 30% respectively.

To calculate the expected value, multiply each outcome by its probability, and then sum up the results:

(-1000 * 0.1) + (-200 * 0.2) + (0 * 0.2) + (200 * 0.2) + (2000 * 0.3) = -$193.

Therefore, the expected value of the investment is -$193.