Probability Lab

How to use it

Choose a coin, one die, two dice or a spinner. Make a prediction first, then run trials: 1 or 10 at a time to watch each result, 100 or 1000 to see the big picture. The bars show what actually happened; the dashed lines show what probability predicts. The table gives the same numbers as fractions and percents.

With the spinner, change the labels, colours and sizes of the sections. A section with size 2 is twice as big as one with size 1, so it should come up about twice as often.

Probability and the law of large numbers

The theoretical probability of a result is the number of ways it can happen divided by the number of equally likely outcomes. A fair coin lands heads 1 out of 2 times. Two dice have 36 equally likely combinations, and 6 of them add to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), so a sum of 7 has a probability of 6/36, or 1/6. Only one combination makes 2 or 12.

The experimental probability is what you actually observe: count divided by trials. In a small number of trials it can be far from the theory (three heads in a row is common). The law of large numbers says that as the number of trials grows, the observed fractions settle closer and closer to the theoretical ones. Watch the "biggest gap" number shrink as you add hundreds of trials. Each single flip is still unpredictable: the coin does not "remember" past flips or try to even things out.

• Ask before running: "If we flip 10 times, will we get exactly 5 heads?" Then try it a few times.
• Why is 7 the most common sum but 1 impossible with two dice?
• Design a spinner where red wins about 3 times out of 4. What sizes did you use?

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