Definition

1. Probabilities are ratios. It is usually written as a proper fraction, but can also be expressed as a decimal or a percentage.
2. Probability is a measure of how likely it is for an event, E, to happen. It is denoted by P(E). 

*P(E) = Number of favourable outcomes for event E / Total number of possible outcomes

Sample question: In a deck of 52 cards, what is the probability of a King card being drawn?

There are 4 King cards in a deck, and 52 cards in total.
Thus P (a King card being drawn) = 4/52 = 1/13.

Properties of Probability

1. P(E) = 0 if E is an impossible event.
E.g. The probability of throwing a die and getting 7 is 0/6, which is 0.

2. P(E) = 1 if E is a certain event.
E.g. The probability of throwing a die and getting a number smaller than 7 is 6/6, which is 1.

3. 0 ≤ P(E) ≤ 1. Any probability lies between 0 and 1 inclusive. 
The closer it is to 0, the more unlikely the event is to happen; the closer it is to 1, the more likely it is to happen.

4. P(E) + P(E’) = 1 OR P(E) = 1 - P(E’)
The complementary event to event E, denoted by E’, contains all the outcomes of the sample space that are not in E. 

The following video serves to reinforce your understanding of how to present probabilities. 

Possibility Diagrams

We use a possibility diagram to represent the sample space when a random experiment involves two stages. Watch the following video to see how this is done:

Tree Diagrams

When a random experiment consists of two or more stages, we use a probability tree diagram to represent the process. Watch the following video to see how this is achieved:

Addition of Probabilities

For two mutually exclusive events A and B, the probability of A OR B occuring is P(A or B) = P(A) + P(B).
Mutually exclusive means that the events cannot happen at the same time.

When solving, take note of the command word "OR". "or" indicates that addition of probabilities is to be used, whereas you will later learn that command word "AND" indicates that multiplication of probabilities is to be used. 

Watch the following video to see a worked example:

Multiplication of Probabilities

For two independent events A and B, the probability of A AND B occuring is P(A and B) = P(A) x P(B).
Events A and B are independent events if the occurrence of one of them does not influence the occurrence of the other.

When solving, take note of the command word "and".

Watch the following video to see a worked example: