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## Glossary

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# ProbabilityWhat are Probabilities

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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 impossiblecertain that you will meet a real life dragon, and it is certainimpossible that the sun will rise tomorrow. The probability of a coin landing heads is exactly in the middlethe same.

The probability of rolling a 6 on a die, or picking a particular suit from a deck of cards is lessmore than 0.5 – which means unlikely. The probability of a good football team winning a match, or of a train arriving on time is moreless than 0.5 – which means likely.        Here are some more events: drag them into the correct order, from likely to unlikely:

You throw a die and it lands on 6.
Penguins live on the North Pole.
It’s going to rain in November.
A baby will be born in China today. You buy a lottery ticket and win the Jackpot .
A newborn baby will be a girl .

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 12 = 0.5, or 50%.

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 approximately halfexactly halfallnone of the results are heads – but we have no way of predicting 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 still 50%100%not 50%.

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.