Compound

also called joint probability
The term compound probability refers to the probability of two or more events happening at the same time.
When you want to calculate the probability of multiple events you need to combine the probabilities of the individual events.
Exactly how these probabilities are combined depends on whether the events are independent and/or mutually exclusive.

Independent Two events are independent if the occurrence of one in no way affects the occurrence of the second event.
Dependent - Two events are dependent if the occurrence of one event changes the probability of the second event.
Mutually Exclusive - (Disjoint) Two events are mutually exclusive if they cannot occur at the same time.

Intersection - AND

Two events are said to be independent if they cannot occur at the same time.
If 2 events are independent then the probability of them both occurring is the product of the individual events.

Independent Events

The probability that event A and B is the probability of the intersection of A and B.

What is the probability of pulling an ace from a pack of cards and then subsequently pulling another ace (assuming the first ace was returned to the pack) (ie sampling with replacement).

Venn diagram
A venn diagram is made up of a square which represents all the possible outcomes.
The individual events are represented by circles inside the square.

Union - OR

Two events are said to be mutually exclusive if the occurrence of one event will exclude the occurrence of the other event.
The two events cannot occur at the same time.
Also known as the addition rule
This basically means that only one event can occur.
If 2 events are mutually exclusive then the probability of either of the events occuring is the sum of the individual probabilities.

What is the probability of pulling an ace from a pack of cards

The probability of not drawing an ace is the complement of pulling an ace (92.31%).

Venn diagram

If two events are combined, the probability of one of them (or both) occurring is the sum of the individual events minus the probability that they will both occur. ???

Mutually Exclusive

If A and B are events then A N B = empty set
EQ