📚 Practice With Worksheets
Practice theoretical probability, experimental probability, relative frequency, and sample spaces with these related worksheets.
▶️ Learn With Videos
Review theoretical and experimental probability with coins, spinners, and dice, then connect repeated trials to long-run outcomes.
🛠️ How to Use This Tool
Choose a batch of 1, 5, 10, 50, or 100 coin flips. Small batches animate each flip, while larger batches run quickly and report the totals.
Compare the theoretical probability of each outcome with the experimental probability, percentage, difference, and streak information shown after the trials.
Use the graph and recent-flips display to study how the results change over time. Select Hide Controls when more space is helpful for projection or discussion.
🧠 Things to Notice
The theoretical probability of heads is \(\frac{1}{2}\), or 0.5, and the theoretical probability of tails is also \(\frac{1}{2}\), or 0.5.
Experimental probability may be far from 0.5 after only a few flips. As the number of trials increases, the experimental probabilities often move closer to the theoretical probabilities.
Heads and tails are complementary outcomes. Their counts add to the total number of flips, and their experimental probabilities always add to 1.
📘 Vocabulary
Probability: A number from 0 to 1 that describes how likely an event is to occur.
Probability Continuum: A scale from 0 to 1, where 0 represents impossible and 1 represents certain.
Outcome: A possible result of an experiment. The outcomes of a coin flip are heads and tails.
Sample Space: The set of all possible outcomes. For one coin flip, the sample space is {heads, tails}.
Event: An outcome or group of outcomes of interest.
Theoretical Probability: The probability expected from analyzing the possible outcomes.
Experimental Probability: The probability calculated from the results of an experiment or simulation.
Trial: One repetition of an experiment. One coin flip is one trial.
Relative Frequency: The fraction, decimal, or percent of trials in which an outcome occurs.
Complementary Outcomes: Outcomes that together make up the entire sample space, such as heads and tails.
Law of Large Numbers: The principle that experimental results tend to approach theoretical probabilities as the number of trials increases.
📐 Probability Rules and Concepts
A fair coin has two equally likely outcomes, so each outcome has a theoretical probability of one-half.
Experimental probability compares the number of times an outcome occurs with the total number of trials.
Because heads and tails are complementary outcomes, their probabilities combine to make the entire sample space.
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