Probability is a numerical value that measures the uncertainty that a particular even will occur.

Probability is the proportion of times that the event can be expected to occur.

An event is the uncertain outcome of an experiment.

The sample space is all the possible outcomes of an experiment.

An elementary events are independent or separate events.

A composite event is an event made up of a grouping of elementary events, the possible outcomes of all three coins tossed together is a composite event.
 

The event set is the possible outcome of an event. It can have the following values:

(1) A single element: Queen of Hearts from a deck of cards: {Q}

(2) Multiple element also called a Finite set: Dimes is a Head in 3 coin toss: {H_pH_nH_d , H_pT_nH_d , T_pH_nH_d , T_pT_nH_d }

(3) An impossible event: Not getting a 1, 2, 3, 4, 5, 6 in the roll of a die: { } or , this is called the empty set of null set.

(4) Impossible event: are also denoted by 0, Pr[impossible event] = 0

(5) Certain event: An even that is always; the sun rising tomorrow, Pr[certain event] = 1

               Pr[certain event] = 1

The Law of Large Numbers states that the probability of an event deviating significantly from its expected or theoretical probability becomes smaller as the number of repetitions of the experiment increases.

An objective probability is a proportion or quantity obtained from repeatable random experiments, such as those discussed above.

A subjective probability is based on judgment and not obtained from non repeatable circumstances.

Compound Probability Events

A compound event is an event that is expressed in terms of other events.

A Venn diagram is a graphical representation of events and their sample space.
 

Mutually Exclusive Events are events that cannot occur together.

Union: (A or B) - Events A or B occurring if either A occurs or B occurs or both occur.

Intersection: Events A and B intersect if they both occurs at the same time. Also called joint probability.

The complement of A is the event that event when it occurs event A does not occurs and when A occurs it does not occur.

Conditional Probability is the probability of an event given the occurrence of another event. It is written as Pr[A|B] meaning the probability of event A occurring given ("|") that event B has already occurred.

The Probability Tree Diagram is a convenient way of showing the conditional probabilities of successive events.

Combinatorics

Combinatorics is the study of counting techniques. In probability is helps to find the size of the sample space.

The n-th factorial is the product of all positive integers (counting numbers, 1, 2, 3, 4, up to n) and is written as n!

The principle of multiplication states that the number of possibilities or sequence of n items is: n!

The permutation is the possible arrangements of items according to the their sequence. 

Combination is the collection of r items taken from a set of n items where the particular items are included and not their sequence.