Experimental vs Theoretical
Run repeated probability experiments and compare experimental (relative frequency) results with theoretical predictions; understand and demonstrate that as the number of trials increases, the experimental probability tends towards the theoretical probability — and that short runs can give very different results
What a learner can do afterwards
- Roll a die 60 times and compare experimental frequencies with the expected 10 per number
- Explain why experimental results don't exactly match theoretical predictions but get closer with more trials
- Predict what would happen if the experiment were repeated 600 times instead of 60
The lesson
You know how to work out theoretical probability, like a 1 in 6 chance of rolling a 3. Theoretical probability is what should happen, based on the math. Experimental probability is what actually happens when you try the experiment for real and count the results.
Zara flips a coin 10 times and gets 7 heads. That is not 50:50, but it does not mean heads is more likely. With only 10 flips, results bounce around a lot. If Zara flipped the coin 600 times instead, the results would land much closer to half heads and half tails.
The more times you repeat an experiment, the closer the experimental probability usually gets to the theoretical probability. A few trials can look uneven. Hundreds of trials smooth out.
Short experiments can look uneven, but more trials pull the results closer to the theoretical probability.
Watch it
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.