# Probability

### Definitions

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

### Vocabulary

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

THE ADDITIVE RULE

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 MULTIPLICATIVE RULE

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. (If.......is true,
what is the probability .....is also true.)