Events and probabilities

The table below gives some examples of events and how their probability can be calculated.

Event	Outcome	Number of ways to get this outcome	Total number of possible outcomes	Probability of outcome
Throwing a fair, 6-sided die	Getting an odd number	\(3\)	\(6\)	\(\frac{3}{6}\)
Throwing a fair coin	Getting 'tails'	\(1\)	\(2\)	\(\frac{1}{2}\)
Choosing a playing card from a full pack without looking	The suit being spades	\(13\)	\(52\)	\(\frac{{13}}{{52}}\)
Choosing a playing card from a full pack without looking	The card being a 'ten'	\(4\)	\(52\)	\(\frac{{4}}{{52}}\)
Throwing a fair, 6-sided die	Getting a number less than \(5\)	\(4\)	\(6\)	\(\frac{{4}}{{6}}\)

Event	Throwing a fair, 6-sided die
Outcome	Getting an odd number
Number of ways to get this outcome	\(3\)
Total number of possible outcomes	\(6\)
Probability of outcome	\(\frac{3}{6}\)

Event	Throwing a fair coin
Outcome	Getting 'tails'
Number of ways to get this outcome	\(1\)
Total number of possible outcomes	\(2\)
Probability of outcome	\(\frac{1}{2}\)

Event	Choosing a playing card from a full pack without looking
Outcome	The suit being spades
Number of ways to get this outcome	\(13\)
Total number of possible outcomes	\(52\)
Probability of outcome	\(\frac{{13}}{{52}}\)

Event	Choosing a playing card from a full pack without looking
Outcome	The card being a 'ten'
Number of ways to get this outcome	\(4\)
Total number of possible outcomes	\(52\)
Probability of outcome	\(\frac{{4}}{{52}}\)

Event	Throwing a fair, 6-sided die
Outcome	Getting a number less than \(5\)
Number of ways to get this outcome	\(4\)
Total number of possible outcomes	\(6\)
Probability of outcome	\(\frac{{4}}{{6}}\)

You may sometimes need to list all the possible outcomes of an event.

The key is to work systematically - do not just list all the outcomes randomly.

Here is an example:

Question

Imagine that you had to find all the different orders in which three people (Anita, Benita and Carol) could finish in a race.