Events and probabilities

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

EventOutcomeNumber of ways to get this outcomeTotal number of possible outcomesProbability of outcome
Throwing a fair, 6-sided dieGetting an odd number 3 6 \frac{3}{6}
Throwing a fair coinGetting 'tails' 1 2 \frac{1}{2}
Choosing a playing card from a full pack without lookingThe suit being spades 13 52 \frac{{13}}{{52}}
Choosing a playing card from a full pack without lookingThe card being a 'ten' 4 52 \frac{{4}}{{52}}
Throwing a fair, 6-sided dieGetting a number less than 5 4 6 \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.

The first step (to save you writing too much) is to label the people A, B and C - but make sure you mention this.

Jot down the different orders in which Anita, Benita and Carol could finish.

ABC, ACB, BCA, BAC, CAB, CBA

Make sure you can 'see' the pattern in the order of choices.