Scientists: champion coin tossers

What is probability?

Ask people what probability is, and chances are they’ll say something about random events like tossing a coin. They might say the probability of getting heads is 50:50, or of rolling a six on a die is one in six. But asked for more examples, they’re likely to start talking about altogether fuzzier things, like the probability of Spurs winning the League, say, or of scientists finding a cure for cancer.

This reflects the odd fact that while the rules governing probability are clear-cut, its exact meaning isn’t – and pinning it down has caused huge controversy.

It’s often useful to regard probabilities as frequencies: the number of times you get the outcome you’re interested in, divided by the total number of opportunities it was given to occur. If a coin is fair, there’s no reason to think heads are more likely than tails, so you’d expect around 50 per cent of all tosses to give heads. Probability laws then give insight into all kinds of outcomes, from the chances of getting 10 consecutive heads to the plausible range for the number of tails seen after 100 tosses.

But how do we know the coin really is fair? The obvious way to find out is to toss the coin and measure the proportions of heads and tails. The laws of probability can then be used to turn the data into a measure of the chances of our belief that the coin is fair being correct. Yet now probability has taken on a different meaning. It’s no longer about objective frequencies but about subjective beliefs. Worse still, it could take on different values for different people, reflecting their personal levels of trust or scepticism.