Question

Imagine an investment with 3 possible outcomes. There's a 10% chance you'll LOSE the $1,000 you put in. There's an 80% chance you'll earn a $100 profit, and a 10% chance you'll earn a $300 profit. What is the expected value of making the investment?

Answer 1

In this case, the expected value of a discrete random variable is equal to the sum of the probability of occurrence of each event multiplied by the value of the result of said event.

Then, the possibilities of dollar gains multiply by their probability of occurrence and add up. In this way, the expected value in this problem is:

$0.1 * (-1000 ) + 0.8 * (100 ) + 0.1 * (300 ) = 10$

Finally, the expected value of making the investment is $ 10 net profit.