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Practice spinner probability, theoretical and experimental probability, and compound events with the resources below. The 🛠️ icon identifies a companion worksheet designed specifically for use with the interactive tool above.
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Review theoretical versus experimental probability and strengthen your understanding of compound events with the related lessons below.
🛠️ How to Use This Tool
Choose Equal Parts to explore spinners divided into halves, thirds, fourths, fifths, or sixths, or choose Unequal Parts to compare sections with different probabilities. Select Single Event or Compound Event to change the question type.
Select New Question + Spinner for a different spinner setup and a new theoretical-probability question. Enter an exact fraction or an appropriately rounded decimal or percent, then select Check. Change your response before checking again, or generate a new question to continue.
Use Spin to collect experimental results in the recent-spin history. Turn fraction labels on or off, compare the experimental outcomes with the theoretical probabilities, and use Hide Controls when you want a larger spinner view.
🧠 Things to Notice
The questions ask for theoretical probability, which is calculated from the spinner model. The colored pills under Most Recent Spins are experimental results produced by actually spinning.
Equal sections have equal probabilities. On an equal spinner with \(n\) sections, each color has probability \(\frac{1}{n}\). On an unequal spinner, larger sections have greater probabilities than smaller sections.
In one-spin questions, the word or means that more than one color is favorable. In compound questions, words such as and, then, first, and second describe outcomes across multiple independent spins.
📘 Vocabulary
Probability: A number from 0 to 1 that describes how likely an event is to occur.
Outcome: A possible result of a probability experiment.
Event: One outcome or a group of outcomes being considered.
Sample Space: The complete set of possible outcomes.
Theoretical Probability: Probability calculated from a mathematical model before an experiment is performed.
Experimental Probability: Probability based on the results observed after an experiment is performed.
Favorable Outcome: An outcome included in the event being studied.
Complement: All outcomes that are not included in a given event.
Compound Event: An event involving two or more actions or outcomes.
Independent Events: Events in which one result does not change the probability of another result.
Mutually Exclusive: Outcomes that cannot occur at the same time during one trial, such as landing on red and blue in one spin.
Most Likely: The outcome with the greatest probability.
Least Likely: The outcome with the smallest probability.
Equally Likely: Outcomes that have the same probability.
Relative Frequency: The fraction or percent of trials that produce a particular outcome.
📐 Probability Rules: When Do You Add or Multiply?
Start with favorable outcomes over total outcomes. For a spinner, compare the combined size of the favorable sections with the size of the entire spinner.
\(P(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}}\)
Use addition for OR during one spin. Words such as or and either tell you that several mutually exclusive colors count as favorable. Add their probabilities because the spinner can land on only one color during that spin.
\(P(A\text{ or }B)=P(A)+P(B)\)
Use multiplication for AND or THEN across independent spins. Words such as and, then, first, second, and both times describe a sequence of results that must all occur.
\(P(A\text{ then }B)=P(A)\times P(B)\)
Some compound events use both operations. Add the OR choices within each spin first, and then multiply the probabilities for the separate spins.
\(P((A\text{ or }B)\text{ then }(C\text{ or }D))=[P(A)+P(B)]\times[P(C)+P(D)]\)
Use subtraction for a complement. The probability that an event does not occur equals 1 minus the probability that it does occur.
\(P(\text{not }A)=1-P(A)\)
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