## Investigation

### Goal

To test the hypothesis that heads and tails are equiprobable. In other words, a flipped coin will land heads up, on average, 50 percent of the time.

### Research question

1. A flipped coin has the equal probability of landing heads up or tails up.
2. There is a coin somewhere in the world that will land significantly more often with either heads or tails up.

### Equipment

1. A modern metal coin
2. A ruler with a millimeter graduation
3. A photo camera (the camera in a smartphone, tablet, or laptop will do)

### Why use data from multiple participants?

1. In statistics, the number of tests always affects the results' reliability. The more tests, the more reliable the results.
2. We're looking for a modern coin with an unequal probability of landing heads and tails when tossed. It must be not a false or defective coin, but a regular coin of a certain type and denomination.

### Investigation Protocol

1. Obtain an ordinary metal coin (not a souvenir or commemorative one). Photograph it against a millimeter-graduated ruler, first the heads side (which will not show its value), and then the tails side (which will show its value).

Tails:
3. On a piece of paper, draw a table:
4. Toss the coin into the air, not too vigorously, so that is goes up about 50 cm. Let it land on a smooth surface, e.g., a table or the floor. The surface must not be elastic, too hard, slippery or viscous. For example, a glass table should be covered with a cloth. Do not allow the coin to hit a wall or any other object other than the table or floor on which it lands. (Safety tip: do not toss the coin about your head or throw the coin. Always keep it in sight.)
5. When the coin lands, observe which side is facing up. If it is heads, put a checkmark in the second column of your table’s first row. If it came up tails, enter nothing in the table.
6. Repeat the toss and put a checkmark in the right column of the second row only it the coin landed heads up.
7. Toss the coin from 20 to 100 times (important: the number of tosses should be an even number) and record if it lands heads each time.
8. Add up the number of “heads” in the right column and divide this number by the total number of tosses in the left column. This will provide the ratio of “heads” to the total number of tosses.
9. Fill in the Report Form.
10. This experiment can be repeated with a different coin.
11. Check the Project’s progress on the Findings page. At what point could we view our common results (yours and other participants) as statistically valid and non-accidental? Will we find an “unfair” coin? How can we be sure this is really an unfair coin and not a mistake in our experiment or just accidental luck?

### Safety tips

Do not toss the coin over your head or behind you, and do not throw the coin. Do not lose sight of the coin.

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• Project was published on:August 21, 2013