Probability simulator

What the simulator does

A probability simulator runs chance experiments faster than any classroom can. Pick a coin, a die numbered 1 to 6, or a spinner with 4 equal colored parts, then press Do it once, 10 times or 100 times. A tally table and bar chart show the results, and each outcome's experimental probability appears as a fraction and a percent next to the theoretical one. Reset clears everything.

Theoretical probability comes from equally likely outcomes: heads on a fair coin is 1/2, or 50%; each number on a fair die is 1/6, about 16.7%; each color on the spinner is 1/4, or 25%. Experimental probability is what actually happened: the number of times an outcome came up divided by the number of tries.

Why run experiments

Common Core standard 7.SP.C.6 asks students to approximate a probability by collecting data from a chance process and watching its long-run relative frequency. Flipping a real coin 100 times takes most of a lesson; here it takes a click, so students can repeat the experiment and see the pattern. The more trials, the closer the experimental probability tends to get to the theoretical one, though it is never guaranteed to match exactly. Standard 7.SP.C.7 then asks students to compare a model with what they observe and explain any differences.

Common mix-ups

• "Tails is due." A coin has no memory. After five heads in a row, the next flip is still 1/2 heads.
• "Ten flips should give five heads." Exactly 5 heads in 10 fair flips happens about 1 time in 4: 252 of the 1,024 equally likely sequences.
• "Six is the hardest number to roll." It can feel that way when a game needs a 6, but every face of a fair die is equally likely.
• "More trials makes the counts even." It is the fractions that tend to settle near 1/2. The gap between the number of heads and tails can still grow.

A 10-minute probability lesson

• Choose the coin. Ask for a prediction for 10 flips, then flip 10 times and write the fraction of heads.
• Reset and repeat a few times. Results like 3, 6 and 7 heads are normal for small samples.
• Now flip 100 times, then another 100, and watch the percentage of heads.
• Switch to the die and predict the number of 6s in 100 rolls. About 17 is a good estimate, since 100 ÷ 6 is about 16.7.
• Ask: if a friend rolled 30 sixes in 100 rolls, would you trust the die? It is possible but far more than expected, so it is worth checking.

Where it fits by grade

• Grades 5 and 6: practice writing results as fractions and percents, and use the language of likely, unlikely, certain and impossible. Common Core does not start formal probability until grade 7.
• Grade 7: probability as a number from 0 to 1 (7.SP.C.5), long-run relative frequency (7.SP.C.6) and probability models (7.SP.C.7).
• England: probability is not part of the primary curriculum. In Key Stage 3 (Years 7 to 9), students record and analyze the outcomes of simple experiments, discuss fairness, use the 0 to 1 scale and learn that the probabilities of all outcomes add to 1. Relative frequency continues at GCSE.

Learning more

Fractions and percentages are skills on Eurekami's skill map, and Daily Practice brings them back when they start to fade. For older students, Exam Prep includes GCSE Maths practice papers, and the AI tutor asks guiding questions when a probability problem is tricky.