ChanceLab makes it easy and quick to develop your instincts about probability. (Click the image at right for a closer look.) Run experiments from a few trials to a few thousand using a coin, 3-, 4-, or 5-part spinners, or a die. Display the results as a bar chart, a pie chart, a line graph or a table of detailed results.

We develop a feel for how things work by by constant play in childhood and by accumulating a lot of experience as adults. Out of all this activity come understandings we can express in words or symbols, and also 'conceptual understandings,' more diffuse, rough senses of the workings of our world.

For many topics in math or science, it's easier to gain understanding in the realm of symbols than it is to develop a solid instinct about things based on experience. Probability is one such topic. Most people simply lack the experience needed to build a rough idea of what should happen in different probabilistic situations.

Use ChanceLab! Test your understanding by running the same experiment several times. What are the similarities? The differences? The surprises? It shouldn't take long to develop a much better feeling for how probability works.

Follow these steps to run an experiment. (Click the image for a closer look.)

1. Choose an object or game piece to experiment with: a coin, a game spiinner, or a die.
2. Choose a number of trials to run, from 1 to 1000.
3. Click the Run button. The results appear in a table at upper left, and the total trials in the yellow box. You can change the number of trials between runs.
4. Click one of the chart icons below to display the results as a bar chart, pie chart, line graph, or detailed table of each trial.
5. Click the Run button more times to see how results change with increasing numbers of trials. Click the Clear button to repeat an experiment, or set up a new one.

Example
The four screenshots below show the results of running a 50-trial experiment with a die. Each display has a slightly different story to tell. (Again, click the image to see a closeup.)

• The bar chart shows that even after 50 trials the six outcomes occurred in very different numbers, even though each outcome has the same probability of occurring. How many trials would it take to even out the bars?
• The pie chart tells much the same story, with the percentages of each outcome listed more clearly on the chart. The pie chart is especially useful when experimenting with a game spinner, which has equal segments with which the experimental results can be compared.
• The line graph shows the result of each of the 50 trials, starting with the first toss which came up 5 dots (purple) and so 100%, followed by 2 dots (yellow) at 50% and so on. Notice that there's quite a bit of variation, but all the traces are moving together around 15 - 20%. This makes sense because the theoretical probability of each outcome is 1/6 = 16.67%. How many trials until the lines overlap at that percent? Will they ever deviate after that?
• The table shows the result of each successive trial. It shows particularly that for six possible outcomes, the chance of a long run of the same result (e.g., four dots) is quite small; only runs of two trials are likely to appear at all. Compare this with a coin flip, where a run of five or six heads or tails is easily possible. Why is that?

It's unlikely you'll need support in using ChanceLab, but if you do, please use the Contact page to send me a message.