Probability Rules

We have five basic probability rules that we must follow when determining the probability of an event or events. Say we have a random event x or two random events x and y. The five basic probability rules are:

1. All probabilities must be between 0 and 1. We can't have anything greater or less, because that doesn't make sense.
0 < P(x) < 1

2. Probabilities that don't have any outcomes in common are said to be DISJOINT or MUTUALLY EXCLUSIVE.

3. Complement probability is the opposite - the probability if it doesn't happen.
P(not x) = 1 - P(x)

4. Multiplication Rule (union): Probability of x AND y happening at the same time.
P(x and y) = P(x) times P(y)

5. Addition Rule (intersection): Probability of x OR y happening, but not both of them at the same time.
P(x or y) = P(x) times P(y) - P(x and y)