Previously, we have used models to describe all sorts of relationships, so now we are giving a mathematical model to probability. A probability model for random phenomenon consists of a sample space S (all possible outcomes) and an assignment of probabilities.
Basically, it works similar to a function. P(A) returns a probability to an event A. Similarly, there is an event Ac, the complement, which is made up of all the outcomes that are not in A. So, if an event W had a .4 probability of occuring, its complement would have a .6 probability of occuring.
Some other important terms to know when dealing with probabilities and the probability model is disjoing and independent. Two events A and B are called disjoint if they have no outcomes in common. Two events A and B are independent if knowing that one event occurs does not change the probability of the other event occuring.
Now, with all the terms established, we move on to the basic properties of probability:
- The probability of any event is between zero and one.
- The probability of the sample space is one
- One minus the probability of the complement of an event is equal to the event.
- The probability that one event A would occur or the probability of one event B would occur is equal to their individual probabilities added together.
- If A and B are independant, then the probability of event A and event B occuring is equal to their individual probabilities multiplied.