Dice and coin investigations help you see probability in action using simple game materials. By rolling two dice 50 times and flipping a coin 100 times, you can collect real data and look for patterns. This project matters because probability helps us make predictions about games, science experiments, weather, and everyday choices.
A tally sheet and calculator make it easier to organize results and compare them fairly.
Key Facts
- Probability = number of favorable outcomes / total number of possible outcomes.
- For one coin flip, P(heads) = 1/2 and P(tails) = 1/2.
- For one fair six-sided die, P(rolling a 4) = 1/6.
- With two dice, there are 36 possible ordered outcomes because 6 x 6 = 36.
- The most likely sum with two dice is 7 because it can happen in 6 ways.
- Experimental probability = number of times an event happens / total number of trials.
Vocabulary
- Probability
- Probability is a number that describes how likely an event is to happen.
- Trial
- A trial is one repeated action in an experiment, such as one dice roll or one coin flip.
- Outcome
- An outcome is a possible result of a trial, such as heads or a dice sum of 8.
- Theoretical probability
- Theoretical probability is the expected chance of an event based on all possible outcomes.
- Experimental probability
- Experimental probability is the chance of an event based on the data you actually collect.
Common Mistakes to Avoid
- Expecting exact results every time is wrong because probability predicts long-term patterns, not perfect short experiments.
- Forgetting to count all trials is wrong because the total number of rolls or flips is the denominator in experimental probability.
- Treating all two-dice sums as equally likely is wrong because some sums, like 7, can be made in more ways than others.
- Changing the method during the experiment is wrong because different rolling or flipping methods can make the data less fair.
Practice Questions
- 1 You flip a coin 100 times and get heads 57 times. What is the experimental probability of heads as a fraction, decimal, and percent?
- 2 You roll two dice 50 times and get a sum of 7 on 9 rolls. What is the experimental probability of rolling a 7, and how does it compare with the theoretical probability 6/36?
- 3 A class rolls two dice and finds that the sum 12 happened more often than the sum 7 in only 20 rolls. Explain why this result can happen and what you would expect if the class rolled many more times.