Question

A game has 3 possible outcomes, with probabilities p 1, p 2, and p 3. The amount of money that you will win or lose for each outcome is v 1, v 2, and v 3, respectively. What is the expression p 1 v 1 + p 2 v 2 + p 3 v 3 equal to? The total amount you will win (or lose) in the long run. The average amount you will win (or lose) per game in the long run. The exact amount you will win (or lose) per game. The amount that you will win (or lose) for 3 games.

Answer 1

The answer is the second option or sentence - The average amount you will win (or lose) per game in the long run.

Because v 1, v 2, and v 3 represents the money that you will either win or lose and the three probabilities of the game represented by p 1, p 2, and p 3. By multiplying both, you are getting the average amount of your win or lose in every game.

Answer 2

The expression given above is the summation of product of probabilities and their outcomes.

This sum is equal to the expected value of the game. Expected value shows how much amount a player can win or lose per game on average, if he plays for a long run. Positive value shows the player wins and the negative value shows the player loses.

So, the answer to this question is option B.
The expression is equal to: The average amount you will win (or lose) per game in the long run