probability distributions

A probability function takes some outcome X (in an experiment, say) and assigns some probability p to it, with 0 < p < 1. For example, suppose we flip a coin six times. We want to know the probability of getting X heads. So in this experiment, X = 0, 1, 2, 3, 4, 5 or 6.

Without getting into too much detail on how these seven probabilities are calculated, here is a figure:

Notice how the probability of getting 3 heads is highest. Our intuition should confirm this: we expect to see half of the flips be heads. Getting no heads or all heads is possible, just not too probable.

The name of this probability function (or distribution) is the Binomial distribution. It is a discrete distribution which means it can only take as inputs integer values.

For a probability function to be a valid, each probability must be between zero and one, inclusive, and they all must sum to one. This again agrees with our intuition since a negative probability doesn't make sense, nor can something occur with more than a 100% chance (probability one).

Many probability distributions exist (infinite really), and we choose which one to use based on what we are measuring.

The big picture: we can use mathematical functions to determine how likely an event is to occur.