Maths Misconceptions: Probability

Tossing a coin isn’t as fair as it seems.

The Khan Academy say this:

And they are wrong.

They aren’t alone in thinking the theoretical probability that a fair coin lands on heads is 0.5

The probability of getting a heads when flipped is closer to 51/49.

Some argue that it isn’t about probability but physics.

Mathematician Persi Diaconis urges us to think differently because in the majority of cases, if a coin is heads-up when it is flipped, it will remain heads-up when it lands.

Diaconis (a professor of mathematics and statistics at Stanford University and also once a professional magician) in his paper Dynamical Bias in the Coin Toss, found that a natural bias occurs when coins are flipped, which results in the side that was originally facing up returning to that same position 51 per cent of the time.

But what about a spinning coin?

According to Diaconis, a spinning penny will land tails side up roughly 80 per cent of the time because because the heads side of the penny (on some coins, e.g. with the portrait of Abraham Lincoln on it) is slightly heavier than the tail side and so this causes the coin’s centre of mass to lie more toward the head side than the tail.