FAIR GAME

Fair Game

Definition Of Fair Game

Fair Game is a game in which each player is not more likely to win than another. In other words, in a fair game each player is equally likely to win the game.

Video Examples: iCoachMath Works

Example of Fair Game

The following are examples of a fair game.

Roll a number cube. You win if you roll a 1 or 2. Your friend wins if he rolls a 1 or 2.
Spinning a spinner with equal sections.

Solved Example on Fair Game

Ques: Which is a fair game?

Choices:

A. There are 2 green, 5 black, and 7 blue pebbles in a box. Tom wins if he chooses a blue pebble thrice.
Mary wins if she chooses a green pebble twice.
B. Put 5 red and 2 blue crayons in a box. You win if you pick a red crayon. Your friend wins if he picks a blue crayon.
C. Toss a coin twice. You win if you get head both times and your friend wins if he gets tail both times.
D. Toss a coin ten times. You win if you get head always and your friend wins if he gets 5 heads and 5 tails.
Correct Answer: C

Solution:

Step 1: Out of the games listed, only 'Toss a coin twice. You win if you get head both times and
your friend wins if he gets tail both times.' is a fair game. Because, when you toss a coin,
head and tail are equally likely to show up.

Quick Summary

In a fair game, all players have the same chance of winning.
Fair games are based on equally likely outcomes.
Examples include spinning a spinner with equal sections or a coin toss with unbiased coin.

\[ P(player_i \text{ wins}) = \frac{1}{n}, \text{ where } n \text{ is the number of players} \]

🍎 Teacher Insights

Use real-world examples of games to illustrate the concept of fairness. Emphasize the importance of calculating probabilities rather than making assumptions.

🎓 Prerequisites

Basic probability concepts
Understanding of equally likely events

Check Your Knowledge

Q1: Which of the following is a fair game?

A. Rolling a die. You win if you roll a 6, your friend wins if they roll a 1 or 2. B. Flipping a coin. You win if it lands on heads, your friend wins if it lands on tails. C. Drawing a marble from a bag with 3 red marbles and 1 blue marble. You win if you draw a red marble, your friend wins if you draw a blue marble. D. Spinning a spinner divided into four equal sections labeled 1, 2, 3, and 4. You win if it lands on 1 or 2, and your friend wins if it lands on 3.

Frequently Asked Questions

Q: How do you determine if a game is fair?
A: Calculate the probability of each player winning. If the probabilities are equal, the game is fair.

Q: Can a game with unequal payouts be fair?
A: Yes, if the probabilities of winning are adjusted to compensate for the unequal payouts, resulting in equal expected values for each player.