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?

Question

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?

Answer 1

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Answer 2

I can't figure out what the other numbers will be.

Answer 3

To determine the fair cost for each roll in the game of dots, we need to consider the expected value. The expected value is calculated by multiplying each possible outcome by its probability and then summing all these values.

In this game, the possible outcomes are the numbers showing on the top face of the die: 1, 2, 3, 4, 5, and 6. Each outcome has an equal probability of occurring since we are rolling a fair die.

Let's calculate the expected value:
Expected Value = (1/6) × 1 + (1/6) × 2 + (1/6) × 3 + (1/6) × 4 + (1/6) × 5 + (1/6) × 6

Simplifying this expression:
Expected Value = (1 + 2 + 3 + 4 + 5 + 6)/6
Expected Value = 21/6
Expected Value = 3.5

Therefore, the fair cost for each roll should be $3.50 to make the game fair.