Experimental Probability
In short: Experimental probability is the chance of an event estimated from real trials, found by dividing the number of times it happened by the total number of trials.
7th GradeProbability7.SP.C.6
What is Experimental Probability?
The experimental probability of an event is the fraction of trials in which it actually occurred. When nobody can count equally likely outcomes in advance, you test and record, so the number is built from data rather than from reasoning.
The formula is \(P(E) \approx \frac{\text{number of times } E \text{ occurred}}{\text{total number of trials}}\). Results can change from one set of trials to the next, but with many more trials they tend to settle near the true value. The estimate can then be used to predict future counts.
How to spot it
- A table or tally lists results of repeated tosses, spins, shots, tests or inspections.
- The problem says based on the data, in the experiment, or what happened in the trials.
- An object is irregular, like a bent coin or a basketball player, so outcomes are not equally likely.
- You are asked to predict how many times something will happen in a future batch.
The method
- Record the number of trials and the number of times the event occurred.
- Divide the occurrences by the trials and simplify.
- Convert to a decimal or percent if needed.
- To predict, multiply the experimental probability by the number of future trials.
Experimental Probability: solved example
Problem
Camila sinks 27 of her 40 free throws in scrimmages. Estimate her chance of making a shot. About how many of her next 120 shots should go in?
Solution
Experimental probability: \(\frac{27}{40} = 0.675\), or 67.5%.
Prediction: \(0.675 \times 120 = 81\). She should make about 81 shots out of 120.
Try it
Question 1
A spinner lands on blue 18 times in 50 spins. What is the experimental probability of blue?
Show the answer
\(\frac{18}{50} = \frac{9}{25} = 0.36\).
Question 2
A factory tests 250 bulbs and finds 7 defective. Predict the number of defective bulbs in a shipment of 4,000.
Show the answer
\(\frac{7}{250} = 0.028\) and \(0.028 \times 4{,}000 = 112\) bulbs.
Experimental Probability vs. Theoretical Probability
Experimental probability comes from what was observed, so it depends on the data and may differ between two experiments. Theoretical probability comes from the structure of the situation and stays fixed. For a fair coin the theoretical value is one half, while a run of 10 tosses may show 7 heads.
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Whole dictionary: A–Z · 7th Grade · Probability