Key takeaway: Experimental probability is an estimate of how likely an event is, based on what actually happened in a set of trials rather than on what should happen in theory.
Grade 77.SP.C.6Probability and Counting
Definition of Experimental Probability
Experimental probability comes from doing the activity and keeping score. If a basketball player shoots 30 free throws and sinks 18, the experiment says her chance of scoring is 18 out of 30. Nobody had to reason about her skill; the record speaks for itself.
This method is the only choice when outcomes are not equally likely or the setup is too messy to analyze, like a thumbtack landing point up or a bus arriving on time. Results vary from one batch of trials to the next, but as the number of trials grows, the experimental value usually settles close to the true chance. A handful of tries can mislead.
Formula and notation
Count the successes and divide by the number of trials:
\[P(\text{event}) \approx \frac{\text{times the event occurred}}{\text{total number of trials}}\]
The sign \(\approx\) reminds us that the value is an estimate that can change with new trials.
Key facts
- The denominator is the number of trials, never the number of failures.
- Doing more trials usually brings the estimate nearer to the true chance.
- Two groups running the same experiment will rarely get identical results.
- The estimate can be used to predict how many successes to expect in a larger run.
Experimental Probability example
During practice, Jamal takes 30 free throws and makes 18. Find the experimental probability that his next shot goes in, and predict how many of 50 shots he should make.
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Made shots over total shots: \(\frac{18}{30} = \frac{3}{5} = 0.6\).
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Scale to 50 shots: \(0.6 \times 50 = 30\).
The chance is 0.6 (60%), so he should make about 30 of 50 shots.
Common mistake
Watch out
Lena compares Jamal’s 18 made shots with his 12 misses and writes \(\frac{18}{12} = 1.5\) as the probability.
Why it is wrong
A probability can never exceed 1, which signals the error. She divided by the failures. The denominator is every trial, 30 in all: \(\frac{18}{30} = 0.6\). Comparing successes with failures gives odds, which is a different measure.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Probability and Counting