Experimental probability from repeated marble draws
MathematicsProbabilityAges 13–14
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Probability
A bag holds red, blue, and yellow marbles; draw one at random, record its color, put it back, and repeat N times. Students draw one marble at a time or let it run automatically, watching a graph of the experimental probability k/n for the chosen event settle toward the theoretical probability (that color's count divided by the total). Click a color to switch which event is being tracked.
Lesson: The experimental probability of an event; the relationship between experimental probability and theoretical probability
What it shows
The experimental probability of an event is k/n, where k is the number of times it occurred in n trials. The simulation draws marbles from a bag with replacement, so every draw happens under the same conditions and the theoretical probability of a color stays fixed at its number of marbles divided by the total. The graph of k/n against n fluctuates strongly for small n and then settles close to the theoretical value, although it rarely equals it exactly. A color with no marbles gives an impossible event, with k/n always 0.
How to use
Set the numbers of red, blue and yellow marbles and ask students to work out each theoretical probability first. Press Draw 1 marble a few times, then Draw 10 marbles, and follow the k/n graph. Use Auto run with a large Maximum number of draws to see the long-run behavior. Click a color in the legend to track another event, and press Reset to compare several runs.
Parameters you can change
- Number of red marbles 0–10 marbles
- Number of blue marbles 0–10 marbles
- Number of yellow marbles 0–10 marbles
- Maximum number of draws 10–2000 draws
- Auto-run speed Slow (watch each draw), Fast, Instant
Questions to explore
- With 3 red, 2 blue and 1 yellow marble, what is the probability of drawing red, and does k/n agree?
- Why must each marble be returned to the bag before the next draw?
- After 20 draws, k/n is far from the theoretical value. Does that mean something is wrong?
