Question

If player A pays player B $1 when the outcome of a die is 1, 2, 3, 4 or 5, how much should player B pay player A when the outcome is 6 in order to make this a fair game?
$ ___

Answer 1

Answer:

player B should pay Player A $30 when the outcome is 6 to make this a fair game.

Step-by-step explanation:

To make the game fair, the amount that player B should pay player A when the outcome is 6 can be calculated by considering the probabilities of each outcome.

There are six possible outcomes when rolling a fair six-sided die: 1, 2, 3, 4, 5, and 6. Each outcome has an equal probability of occurring, which is 1/6.

Player A pays Player B $1 when the outcome is 1, 2, 3, 4, or 5. So, the total amount that player A pays player B for these outcomes is:

Total amount = 5 * $1 = $5

To make the game fair, the expected value for player B's payment when the outcome is 6 should be equal to the total amount that player A pays player B. Since each outcome has an equal probability, the expected value for player B's payment when the outcome is 6 can be calculated as follows:

Expected value = Probability of outcome 6 * Amount of payment

Let's denote the amount that player B should pay when the outcome is 6 as X. Since the game is fair, we can set up the following equation:

(1/6) * X = $5

Solving this equation, we can find the value of X:

X = $5 * (6/1)

X = $30

Therefore, player B should pay player A $30 when the outcome is 6 to make this a fair game.

Answer 2

Final answer:

To make the game fair, player B should pay player A $4 when the outcome of the die is 6.

Explanation:

To make the game fair, player B should pay player A $4 when the outcome of the die is 6. This is because the total amount of money gained by player A should equal the total amount of money gained by player B over the long run.

If player A pays player B $1 when the outcome is 1, 2, 3, 4, or 5, then player A will gain $1 in those cases. In order for player B to also gain $1 in these cases, player B should pay player A $1. So, the net gain for both players is $0 in these cases.

When the outcome is 6, player B should pay player A $4 in order for both players to have a net gain of $0. Here's how the calculation works: Player A gains $1 in the cases 1, 2, 3, 4, and 5. Player B gains $1 in these same cases. In the case of a 6, player B should pay player A $4 so that player A has a net gain of $0. Player B's net gain is $1-$4 = -$3. The total net gain for both players is $0.