# Probability of an event

The probability of an event shows the degree of confidence that we have about the event happening. We express it with a number between 0 and 1.

P(E) = 1, P(Φ) = 0.

Examples: we flip a coin 1000 times or we drop a thumbtack 1000 times, and we obtain:

 Coin fi hi head 483 0.483 tail 517 0.517 Σ 1000 1

 thumbtack fi hi 327 0.327 673 0.673 Σ 1000 1

We see that the relative frequencies in the coin example are close to 0.5. That is logical, and the frequency value is very close to the event probability:

P(H) = P(T) = 0.5

In the other hand, the relative frequencies of the thumbtack case are very different from 0.5 and their probabilities are unknown, but they will certainly be close to relative frequencies we have obtained.

“Law of large numbers”: when we repeat a random experience several times, the relative frequency of obtaining each event is close to its probability.

If we have a regular experiment, as the coin one, we can evaluate the probability a priori, puting the same probability at all the events.
If the experience isn’t regular, we won’t know a priori the probability of the events, and we have to make experiments to find out it.