In day to day life, there are many places where the language of probability is used. For example:
Probability the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the number of cases possible. That is, the probability of an event occurring is:
$P(event)=\frac{\text{number of favourable outcomes}}{\text{total possible outcomes}}$P(event)=number of favourable outcomestotal possible outcomes
The range of values that all probabilities can take is between $0$0 and $1$1, where a probability of zero indicates the event cannot possibly occur and a probability of one indicates the event is certain to occur. This can be visualised as follows:
If all the outcomes can be easily listed, then the process of counting favourable and total outcomes is relatively straightforward. When calculating probabilities for a large or complex set of outcomes we may wish to employ approaches such as tree diagrams or use properties of probability that relate to different characteristics of the event such as the complement of the event.
The sample space, sometimes called an event space, is a listing of all the possible outcomes that could arise from an experiment.
For example:
Notice how the the sample space is listed as a set using curly braces $\left\{\ \right\}${ }. We could also display all outcomes in a sample space by using a table (array) or tree diagram.
An event is the word used to describe a single result from within the sample space. It helps to identify which of the sample space outcomes we might be interested in.
For example, these are all events.
We use the notation $P\left(\text{event}\right)$P(event) to describe the probability of a particular event.
A game in a classroom uses this spinner.
What is the chance of spinning an odd number?
certain
even chance
impossible
likely
What is the chance of spinning a $2$2?
likely
impossible
certain
even chance
What is the chance of spinning a number less than $8$8?
likely
impossible
even chance
certain
A probability of $\frac{4}{5}$45 means the event is:
Impossible
Unlikely
Likely
Certain
A standard six-sided die is rolled.
List the sample space.
(Separate outcomes with a comma)
List the sample space for rolling a number strictly less than $3$3. Separate outcomes with a comma.
List the sample space for rolling a number divisible by $3$3. Separate outcomes with a comma.
List the sample space for rolling an even number. Separate outcomes with a comma.