Experimental Probability and Fair Games
Have you ever wondered if a game is fair? Or what your chances are of winning a game? That's what experimental probability helps us figure out!
What is Experimental Probability?
Experimental probability is what actually happens when we try something many times. It's based on experiments or trials that we conduct in real life.
The formula for experimental probability is:
Experimental Probability = Number of times an event occurs ÷ Total number of trials
For example, if you flip a coin 10 times and get heads 6 times, the experimental probability of getting heads would be 6 ÷ 10 = 0.6 or 60%.
What Makes a Game Fair?
A fair game is one where everyone has an equal chance of winning. In a fair game, the probability of each player winning should be the same.
For example, when you flip a coin, there's a 50% chance it lands on heads and a 50% chance it lands on tails. That makes it fair for two players if one picks heads and one picks tails.
An unfair game is one where some players have a better chance of winning than others.
How to Test if a Game is Fair
To test if a game is fair, we can:
- Play the game many times (conduct trials)
- Record the results
- Calculate the experimental probability
- Compare the results to what we expect in a fair game
The more trials we do, the more accurate our experimental probability will be!
Connecting to Other Math Concepts
Experimental probability connects to:
- Fractions - Probability can be written as a fraction (3/10)
- Decimals - Probability can be written as a decimal (0.3)
- Percentages - Probability can be written as a percentage (30%)
- Division - We divide to find probability
Remember, the more trials we do, the closer our experimental probability usually gets to the theoretical probability (what we expect to happen based on math).