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?
How about $3.50 per roll?
You have 3 chances to lose and 3 chances to win.
How did you get $3.50?
My school is having a Math fair using the strands. we are to make the project fun. I need to know how and what to do. I need help!
my email is
To determine the cost that should be set for each roll to make the game fair, we need to calculate the expected value. The expected value represents the average amount of money a player can expect to win or lose per roll in the long run.
In this game, the cost per roll should be set such that the expected value is zero. If the expected value is positive, the player would have an advantage, and if it is negative, the player would be at a disadvantage.
Here's how we can calculate the expected value step-by-step:
1. Calculate the probability of each outcome:
- When rolling a fair die, there are six possible outcomes: 1, 2, 3, 4, 5, and 6. Each outcome has a 1/6 probability of occurring.
2. Determine the winnings for each outcome:
- The player receives $1 for each dot showing on the top face of the die. Therefore, for outcomes 1, 2, 3, 4, 5, and 6, the winnings would be $1, $2, $3, $4, $5, and $6, respectively.
3. Calculate the expected value:
- Multiply each outcome's probability by its corresponding winnings and sum them up.
The expected value (EV) of the game is given by:
EV = (1/6) * $1 + (1/6) * $2 + (1/6) * $3 + (1/6) * $4 + (1/6) * $5 + (1/6) * $6
Simplifying, we get:
EV = ($1 + $2 + $3 + $4 + $5 + $6) / 6
Adding up the values, we have:
EV = $21 / 6
Therefore, the expected value is $21/6 or $3.50.
To make the game fair, the cost per roll should be set to $3.50. This way, the player's average winnings and cost will balance out, resulting in a fair game.