How-to guide Coin flip

How to Simulate Coin Flips for a Probability Experiment

Here’s how to simulate coin flips for a probability experiment: generate a fixed batch of independent coin flips, count each side, and compare the observed proportions with one half.

How to Simulate Coin Flips for a Probability Experiment

Twenty flips form a small classroom dataset. Students count Heads and Tails after saving the batch. The settings below match the worked example. Change them to match your activity. Nothing is generated until you select Flip coin.

Settings

Configure your result

1–100 flips per batch

Each click generates a new result.

Result

Waiting for input

No result yet

Generate a result using the settings on the left.

Runs in your browser. Your input is not uploaded.1–100 flips per batch

Step-by-step instructions

  1. Set the number of flips

    Use one for a single toss or choose a batch for several independent flips. The maximum is 100.

  2. Assign meanings before flipping

    If heads and tails represent different options, agree on those meanings before seeing the result.

  3. Flip and record the outcome

    Select Flip coin. Use the order shown when interpreting a sequence and save the batch if you need it later.

Worked example

Twenty flips form a small classroom dataset. Students count Heads and Tails after saving the batch.

One valid result is shown below. Your generated outcome will vary.

Example settings

Number of flips: 20

Example result

1. Heads
2. Tails
3. Heads
4. Tails
5. Heads
6. Tails
7. Heads
8. Heads
9. Tails
10. Tails
11. Tails
12. Heads
13. Heads
14. Heads
15. Heads
16. Tails
17. Heads
18. Heads
19. Tails
20. Heads

Divide the number of heads by 20 to obtain the observed heads proportion. It may differ from 0.5 without implying an error.

State the experiment before collecting outcomes

Choose the sample size and what you will measure before generating. A total count and a run-length study need different records, so keep the sequence when order matters. The tool does not calculate cumulative statistics or retain earlier batches. Larger samples can still contain runs and do not guarantee an exact half-and-half split.

Settings and limits to check

Every flip independently selects Heads or Tails with equal probability. A batch is not forced to contain an equal number of each, and earlier outcomes do not make the opposite outcome due. Batch sizes range from 1 to 100. New generations replace the current display and do not keep cumulative counts.

Settings used in this example
Number of flips: 20

Keep a usable copy of the result

Use Copy to place the current result in your own notes, or Download to keep a text file. Keep the range, count, or other settings with the result when they are needed to interpret it. A new generation replaces the displayed result rather than adding to a saved history.

The tool runs in your browser and does not upload your input. Save the result before refreshing or leaving the page. If other people need to use the same outcome, share your saved copy rather than asking them to generate another independent result.

Frequently asked questions

Is a run of five heads impossible in a fair simulation?

No. Runs can occur. An individual run does not force the next outcome or by itself establish that the process is biased.

Will ten flips always contain five heads?

No. Five heads is one possible count, but independent flips can produce more or fewer.

Can several heads occur in a row?

Yes. Runs are possible in independent flips and do not force the next result to be tails.

What should I check in the worked example?

Divide the number of heads by 20 to obtain the observed heads proportion. It may differ from 0.5 without implying an error.