How to explain it
The anchor students hold onto: Experimental: P = favorable trials / total trials. Theoretical: P = favorable outcomes / total outcomes. More trials moves experimental probability closer to theoretical.
Understanding long-run relative frequency leads directly into 7.SP.C.7 probability models, where theoretical probability is used to build and evaluate models of chance.
Worked examples
Example 1
Experimental Probability
Red spun 14 out of 40 times.
Step 1Identify favorable outcomes: 14 reds from the data.
Step 2Total trials: 40 spins.
Step 3P(red) = 14/40. Simplify: 7/20.
AnswerP(red) = 7/20
Example 2
Theoretical Probability
Bag: 3 red, 12 total marbles.
Step 1Sample space: 12 equally likely outcomes.
Step 2Favorable outcomes: 3 red marbles.
Step 3P(red) = 3/12 = 1/4.
AnswerP(red) = 1/4
Example 3
Predicting Outcomes
P(red) = 1/4; 80 spins total.
Step 1Use: expected = P × total trials.
Step 2Substitute: 1/4 × 80 = 20.
AnswerAbout 20 red results
Common mistakes
What students write
Uses the count of unfavorable outcomes as the denominator: P = favorable / unfavorable.
The fix
The denominator must be the TOTAL — all trials or all possible outcomes, not just the ones that did not occur.
Try this
Maya is given data from 50 spinner trials: Red: 18 times, Blue: 22 times, Green: 10 times. She is asked to find the experimental probability of spinning red. Maya’s work: The spinner has 3 colors, so P(red) = 1/3. Identify Maya’s error and show the correct experimental probability.
What students write
Uses theoretical probability (from the sample space) when asked for experimental probability from the data table.
The fix
Experimental probability reads from the actual data: count favorable trials and divide by total trials, regardless of the theoretical value.
Try this
Liam rolls a number cube 30 times. It lands on 3 exactly 7 times. Liam’s work: Threes: 7. Non-threes: 23. P(3) = 7/23 Identify Liam’s error and write the correct experimental probability.
Teacher tip
Head off the two predictable errors before they happen. First: The denominator must be the TOTAL — all trials or all possible outcomes, not just the ones that did not occur. Second: Experimental probability reads from the actual data: count favorable trials and divide by total trials, regardless of the theoretical value.