The game of dots is played by rolling a fair dice and receiving $1 for each dot showing on the top face of the die. What cost should be set for each roll if the game is to be considered a fair game?

How about the mean for the six values?

To determine the fair cost for each roll in the game of dots, we need to consider the expected value. The expected value represents the average amount of money that a player can expect to win or lose in one game. In a fair game, the expected value should be zero.

In this case, a fair die is rolled, and the player receives $1 for each dot showing on the top face of the die. Since a fair die has six sides numbered from 1 to 6, the possible outcomes are 1, 2, 3, 4, 5, and 6 dots.

To calculate the expected value, we need to find the average earnings for each possible outcome and then sum them up.

The probability of rolling each outcome is 1/6 because there are six equally likely outcomes on a fair die.

So, the expected value (E) can be calculated as:

E = (1/6) * 1 dot + (1/6) * 2 dots + (1/6) * 3 dots + (1/6) * 4 dots + (1/6) * 5 dots + (1/6) * 6 dots

Simplifying the equation:

E = (1/6) * (1 + 2 + 3 + 4 + 5 + 6)
= (1/6) * 21
= 3.5

The expected value of rolling the die is $3.5.

For the game to be fair, the cost of each roll should be set at $3.50, as this will result in an expected value of zero.