The game of dots is played by rolling a fair die 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?

Is the average dots

1+2+3+4+5+6 divided by six?

To determine the cost that should be set for each roll in order for the game to be considered fair, we need to calculate the expected value of each roll. The expected value represents the average outcome of a random variable.

In this case, the random variable is the number of dots showing on the top face of the die. Since the die is fair, it has an equal probability of landing on each of its six faces. Each face has a dot count from 1 to 6.

To calculate the expected value of a roll, we need to multiply each possible outcome by its corresponding probability, and then sum these results.

The probabilities for each outcome are:

P(1 dot) = 1/6
P(2 dots) = 1/6
P(3 dots) = 1/6
P(4 dots) = 1/6
P(5 dots) = 1/6
P(6 dots) = 1/6

The corresponding outcomes (in dollars) are:

Outcome(1 dot) = $1
Outcome(2 dots) = $2
Outcome(3 dots) = $3
Outcome(4 dots) = $4
Outcome(5 dots) = $5
Outcome(6 dots) = $6

To calculate the expected value, we multiply each outcome by its probability and sum the results:

Expected Value = ($1 * 1/6) + ($2 * 1/6) + ($3 * 1/6) + ($4 * 1/6) + ($5 * 1/6) + ($6 * 1/6)
= $21/6
= $3.50

Therefore, the cost that should be set for each roll in order for the game to be considered fair is $3.50.