What are the rules of probability?

Basic Rules of Probability:

1) The probability of an event (E) is a number (fraction or decimal) between and including 0 and 1. (0≤P(E)≤1)

2) If an event (E) cannot occur its probability is 0.

3) If an event (E) is certain to occur, then the probability if E is 1. This means that there is a 100% chance that something will occur.

4) The sum of probabilities of all the outcomes in the sample space is 1.

Addition Rules/Formulas:

When two events (A and B) are mutually exclusive, meaning that they can't occur at the same time or they have no outcomes in common, the probability that A or B will occur is:

P(A or B)= P(A)+P(B)

If A and B are not mutually exclusive, then:

P(A or B)= P(A)+P(B)-P(A and B)

Multiplication Rules/Formulas:

When two events (A and B) are independent events, meaning the fact that A occurs does not affect the probability of B occurring (for example flipping a coin, rolling a die, or picking a card), the probability of both occurring is:

P(A and B)= P(A)P(B)

Conditional Probability-When two events are dependent (not independent), the probability of both occurring is:

P(A or B)= P(A)P(B|A)

Note: P(B|A) does not mean B divided by A but the probability of B after A.