Question

Consider the above game with a modification. We would like to make a fair, FREE game..

We will do this by charging a customer money if they roll a 1. If all the rest is the same,
what should we charge if they roll a 1?

Answer 1

To make the modified game fair and free, we need to determine the amount to charge the customer for rolling a 1. This can be done by setting up an equation to ensure each outcome has the same probability. The equation will help us find the amount to charge for rolling a 1.

Step-by-step explanation:

In the modified game, the customer is charged money if they roll a 1. To make the game fair and free, we need to determine the amount to charge for rolling a 1. Since the game has six possible outcomes on a fair die (1, 2, 3, 4, 5, 6), each outcome should have the same probability of occurring. To find the amount to charge for rolling a 1, we can set up an equation to ensure the game is fair. Let's consider an example:

1. Let's say we charge $x for rolling a 1.
2. There are five other possibilities (2, 3, 4, 5, 6) where the customer doesn't get charged anything.
3. The sum of probabilities for all the outcomes must be 1 (100%), as it is a fair game.

The equation we can set up is:
(x * probability of rolling a 1) + (0 * probability of rolling a 2) + (0 * probability of rolling a 3) + (0 * probability of rolling a 4) + (0 * probability of rolling a 5) + (0 * probability of rolling a 6) = 1

Learn more about Probability and fair games