# ProbabilityWhat are Probabilities

A **probability** is a number between 0 and 1 which describes the likelihood of a certain **event**. A probability of 0 means that something is *impossible*; a probability of 1 means that something is *certain*.

For example, it is *heads* is exactly

The probability of rolling a 6 on a die, or picking a particular suit from a deck of cards is

Here are some more events: drag them into the correct order, from likely to unlikely:

We often use probabilities and likelihoods in everyday life, usually without thinking about it. What is the chance of rain tomorrow? How likely is it that I will miss the bus? What is the probability I will win this game?

Tossing a (fair) coin has two possible outcomes, *heads* and *tails*, which are both equally likely. According to the equation above, the probability of a coin landing *heads* must be

Note that this probability is *in between* 0 and 1, even though only one of the outcomes can actually happen. But probabilities have very little to do with actual results: if we toss a coin many times we know that *exactly which* tosses landed heads.

Even events with tiny probabilities (like winning the lottery ) *can still happen* – and they *do happen* all the time (but to a very small proportion of the people who participate).

Probabilities also depend on how much each of us knows about the event. For example, you might estimate that the chance of rain today is about 70%, while a meteorologist with detailed weather data might say the chance of rain is 64.2%.

Or suppose that I toss a coin and cover it up with my hands – the probability of tails is 50%. Now I peek at the result, but don’t tell you. I know for certain what has happened, but for you the probability is

There are many different ways to think about probabilities, but in practice they often give the same results:

The **classical** probability of landing heads is the proportion of *possible outcomes* that are heads.

The **frequentist** probability is the proportion of heads we get if we toss the coin *many times*.

The **subjectivist** probability tells us how strongly we *believe* that the coin will land heads.

Remember that while probabilities are great for *estimating and forecasting*, we can never tell what *actually* will happen.

Now let’s have a look at some fun applications of probability.