📚 Practice With Worksheets
Practice compound probability, sample spaces, and comparisons between theoretical and experimental results with the resources below. The 🛠️ icon identifies a companion worksheet designed specifically for use with the interactive tool above.
▶️ Learn With Videos
Review theoretical and experimental probability, compound events involving dice and spinners, and how probabilities change when outcomes are not replaced.
🛠️ How to Use This Tool
Run 1, 6, 12, or 24 trials to generate a number-cube result and a spinner color for each compound outcome.
Use the outcome card, recent-trial history, and frequency table to track how often each of the 24 possible outcomes occurs.
Toggle between decimal and fraction displays, then compare each experimental probability with the fixed theoretical probability of 1/24.
🧠 Things to Notice
There are 24 possible compound outcomes because each of the 6 number-cube results can be paired with each of the 4 spinner colors.
In a small number of trials, some outcomes may appear several times while others may not appear at all, even though every outcome is equally likely.
As more trials are completed, the experimental probabilities often move closer to the theoretical value, although random variation does not disappear completely.
📘 Vocabulary
Compound event: An event made from two or more simple events, such as rolling a number cube and spinning a color spinner.
Outcome: One possible result of a probability experiment, such as 4 and Green.
Sample space: The complete set of all possible outcomes. This experiment has 24 outcomes.
Theoretical probability: The probability predicted from the structure of the sample space.
Experimental probability: The probability calculated from the results of actual trials.
Frequency: The number of times a particular outcome occurs.
Trial: One performance of the probability experiment.
Law of large numbers: The principle that experimental probabilities tend to approach theoretical probabilities as the number of trials increases.
🎲 Key Probability Concepts
The number cube has 6 possible results and the spinner has 4 possible colors, so the compound experiment has 6 × 4 = 24 possible outcomes.
Because every number and every color are equally likely in this tool, each combined outcome has a theoretical probability of 1/24 ≈ 0.0417 ≈ 4.2%.
Experimental probability is calculated by dividing an outcome’s frequency by the total number of trials. For example, if 3-Blue occurs 5 times in 60 trials, its experimental probability is 5/60 = 1/12 ≈ 0.0833 ≈ 8.3%.
The difference column compares each experimental probability with 1/24. Positive values show outcomes occurring more often than expected so far, while negative values show outcomes occurring less often than expected.
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