Question

A game has 3 possible outcomes, with probabilities p1, p2, and p3. The amount of money that you will win or lose for each outcome is v1, v2, and v3, respectively. What is the expression p1v1 + p2v2 + p3v3 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

That expression is the expected value of your winnings, or "the average amount you will win (or lose) per game in the long run".

Answer 2

Explanation:

Given that a game has 3 possible outcomes, with probabilities p1, p2, and p3

The amount win or lose for each outcome is v1, v2, and v3, respectively.

If X is the amount of win or lose then x has the following prob distribution

`X      v_1       v_2      v_3\\Pr.    p_1       p_2     p_3\\`

Hence Expected value of x = average of x

=
`p1v1 + p2v2 + p3v3`

Thus answer is

Option b) The average amount you will win (or lose) per game in the long run.