Maths
Probability
Probability is about estimating how likely (probable) something is to happen. Probability can be used to predict, for example, the outcome when throwing a die or tossing a coin.
We often use words to describe how probable we think it is that an event will take place. For example, we might say that it is likely to be sunny tomorrow, or that it is unlikely to snow in August.
Have a look at the statements below, and decide whether the following events are: certain, likely, very likely, evens (neither likely or unlikely), unlikely, very unlikely or impossible.
A game is played where 7 beads with digits from 1 to 7 on them are placed in a bag, a bead is taken out, and you then have to guess whether the number on the next one to be taken out will be higher or lower, and so on.
In each case, choose an appropriate word from the following list to complete each sentence:
Remember that there is only one of each number.
Words like 'certain', 'likely', and so on, may not mean the same to everyone. We need to be more precise about how likely something (an outcome) is to happen. The probability of an outcome can have any value between 0 (impossible) and 1 (certain). It may be a fraction, decimal or percentage.
When different outcomes of an event are equally likely (for example, getting a head when you toss a coin), you can use a formula to calculate the probability of outcomes.
When you throw a fair dice there are six possible outcomes: 1, 2, 3, 4, 5 or 6. There are three ways of getting an odd number (1, 3 or 5).
So the probability of getting an odd number =
the number of ways of getting an odd number ÷ total number of possible outcomes = ^{3}/_{6} = ^{1}/_{2} or 0.5, or 50%.
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 dice | Getting an odd number | 3 | 6 | ^{3}/_{6} |
Throwing a fair coin | Getting 'tails' | 1 | 2 | 50% |
Choosing a playing card from a full pack without looking | The suit being spades | 13 | 52 | ^{13}/_{52} |
Choosing a playing card from a full pack without looking | The card being a 'ten' | 4 | 52 | ^{4}/_{52} |
Throwing a fair, 6-sided dice | Getting a number less than 5 | 4 | 6 | ^{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:
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.
Here are two fair spinners. The total score is the sum of the two numbers the arrows point to.
Jot down, systematically, all the possible outcomes for the two spinners. You will find it useful to use a table of results, as shown.
Triangular spinner | Square spinner | Total score |
---|---|---|
1 | 0 | 1 |
1 | 1 | 2 |
1 | 2 | 3 |
1 | 3 | 4 |
2 | 0 | 2 |
2 | 1 | 3 |
2 | 2 | 4 |
2 | 3 | 5 |
3 | 0 | 3 |
3 | 1 | 4 |
3 | 2 | 5 |
3 | 3 | 6 |
Use the table to answer these questions:
How many different possible outcomes are there?
12. All you have to do is count the number of entries in the table.
How many outcomes gave a total score of 2?
Only 2 outcomes give a total score of 2: a '1' on each spinner, or a '2' on the triangular spinner and '0' on the square one.
What is the probability of getting a total score of 2?
The number of outcomes giving a total score of 2 ÷ the total number of outcomes = ^{2}/_{12} or ^{1}/_{6}
What is the probability of getting a total score of 4?
The number of outcomes giving a total score of 4 ÷ the total number of outcomes = ^{3}/_{12} or ^{1}/_{4}
You can estimate probabilities from an experiment. These are sometimes called experimental probabilities.
For example, in an experiment where you drop a drawing pin:
So the probability of the drawing pin landing up is:
The number of times this outcome occurs (pin up) ÷ total number of outcomes (or trials) = ^{279}/_{1000} (or 0.279, or 27.9 %).
Now try a Test Bite