Probability started with games of chance using cards and dice hundreds of years ago. Probability comes from the chance of a particular outcome happening.


 Such an outcome is called a simple event. For example, the desired outcome for a bettor is the simple event of buying the winning ticket for the lottery.

The set of all possible outcomes is called the sample space.  For the lottery there is either having the numbers on the ticket that will win the money (when only one possible ticket has these numbers) or having the ticket that does not have the winning numbers.

Independent events are those events which the occurrence or nonoccurrence of each has no effect on the occurrence or nonoccurrence of the other.

Mutually exclusive events are those when the occurrence of one precludes the occurrence of  the other.  In other words, they cannot happen together.

Basic laws of probability


When 2 events are mutually exclusive, the probability of the occurrence of one event or another is equal to the sum of their separate probability.


The probability of the joint occurrence of two or more independent events is the product of their individual probabilities.

Two more important types of probabilities:

Joint probability is the probability of the co-occurrence of two or more events.  When the events are independent, you use the multiplicative rule.

Conditional probability is the probability that one event will occur given that some other event has occurred.  ( true, what is the probability also true.)