# Influencing a Coin Flip

The purpose of this experiment is to determine first the probability of a coin landing heads or tails and second whether the person flipping a coin can influence the coin to land one way or another.

### Research Questions:

• What does it mean, in the study of mathematics, if something is said to be random?
• What is the statistical probability that a coin, when flipped 100 times, will land heads up 100 times?
• What is the statistical probability that a coin, when flipped 100 times, will land heads up 50 times and tails up 50 times?
• What is the statistical probability that a coin, when flipped 100 times, will alternate between heads and tails each time?
• What is a significant statistical deviation?
• How many trials are needed to view statistically significant results?
• How accurate is statistical data?
• How can statistics be used to mislead?

A coin flip has long been used as an impartial determiner. Given a choice between two options, some people turn to the flip of a coin to tell them which option to choose. Coin flips are sometimes even used to determine which sports team will start with possession of the ball, which can give a significant advantage to one team or the other. Though it seems that over a large number of trials a coin will land heads or tails an even number of times, there are some studies that suggest that a coin flip may not be a truly random event. People influence the world around them in many different ways. It may be possible for the person flipping a coin to alter the trajectory of that coin such that it will land on heads or tails more often than probability would predict.

### Materials:

• A quarter
• A few willing participants

### Experimental Procedure:

1. Flip a coin 100 times. Do not attempt to influence the results in any way, just flip the coin, allow it to land on the floor, a table, or another surface and record the results.
2. Record the results on a chart such as the one below.
3. Flip a coin 100 times, trying to make the coin land heads up. Allow the coin to land on the floor, a table, or another surface.
4. Record the results.
5. Flip a coin 100 times, trying to make the coin land heads up. Catch the coin in the air and flip it upside-down one more time onto the back of your other hand.
6. Record the results.
7. Repeat steps 1-6 with other participants. The more trials you perform, the more accurate your results will be.
 Trial # Attempt to influence? Caught the coin? Heads (keep a running tally) Tails (keep a running tally) 1 (participant 1) No No 2 (participant 1) Yes No 3 (participant 1) Yes Yes 4 (participant 2) No No 5 (participant 2) Yes No

Terms/Concepts: random;probability; statistic; statistical significance; influence results; deviation

References:

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