Probability

Probability is simply how likely something is to happen. Whenever we are not sure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Definition

An experiment is a situation involving chance or probability that leads to results called outcomes.

An outcome is the result of a single trial of an experiment.

An event is one or more outcomes of an experiment.

Probability is the measure of how likely an event is.

The best example for understanding probability is flipping a coin:

There are two possible outcomes—heads or tails.

What’s the probability of the coin landing on Heads? We can find out using the equation $P(H) = ?$P, left parenthesis, H, right parenthesis, equals, question mark.You might intuitively know that the likelihood is half/half, or 50%.  But how do we work that out?  

Probability =

Formula for calculating the probability of certain outcomes for an event

In this case:

Probability of a coin landing on heads

Probability of an event = (# of ways it can happen)                                                                                                       (total number of outcomes)

P(A) = (# of ways A can happen)                                                                                                        (Total number of outcomes)

EXAMPLE:

There are six different outcomes.

Different outcomes rolling a die

What’s the probability of rolling a one?

Probability formula for rolling a '1' on a die

What’s the probability of rolling a one or a six?

Probability of a 1 or a 6 outcome when rolling a die

Using the formula from above:

Probability formula applied

What’s the probability of rolling an even number (i.e., rolling a two, four or a six)?

Probability of rolling an even number? The formula and solution

Tips

• The probability of an event can only be between 0 and 1 and can also be written as a percentage.
• The probability of event $A$A is often written as $P(A)$P, left parenthesis, A, right parenthesis.
• If $P(A) > P(B)$P, left parenthesis, A, right parenthesis, is greater than, P, left parenthesis, B, right parenthesis, then event $A$A has a higher chance of occurring than event $B$B.
• If $P(A) = P(B)$P, left parenthesis, A, right parenthesis, equals, P, left parenthesis, B, right parenthesis, then events $A$A and $B$B  are equally likely to occur.