Basics of probability
In a nutshell
Probability indicates how likely an event is to occur. Probabilities can be described as 'certain', 'impossible' or 'likely', however it is better to give probabilities numerical values, so they can be compared or used in further calculations.
Definition
Probability indicates the chance that an event will occur. It can be used to try and predict the outcome of random events.
All probabilities lie on a probability scale between zero and one, and can be expressed as a fraction, decimal or percentage. A probability of zero means an event will never happen whereas a probability of one means it will definitely happen. All events will have a probability between zero and one.
Formula
Probabilities can be expressed as a fraction, decimal or a percentage.
The probability (P) of an event (A) occurring is given as:
P(A)=Total number of trialsNumber of times event occurs
Example 1
What is the probability of rolling a 6 on a fair die?
There is an equal probability of landing on each of the six sides of a die, hence:
P(6)=61=0.16˙=16.6˙%
Probabilities will also always add up to one since an event must either happen or not.
P(event happening)+P(event not happening)=1
Example 2
A spinner has 3 different sized sides, one yellow, one red and one blue. What is the probability of the spinner landing on yellow? What is the probability of the spinner not landing on yellow?
Colour | Yellow | Red | Blue |
Probability | | | |
First, work out the probability of the spinner landing on yellow:
x+0.3+0.1=1 x=0.4
So, the probability of the spinner landing on yellow is 0.4 or 40%.
Then, work out the probability of the spinner not landing on yellow:
P(event happening)+P(event not happening)=1 0.4+P(event not happening)=1 P(event not happening)=0.6
So, the probability of the spinner not landing on yellow is 0.6 or 60%.
Probabilities of typical random events
Simple probabilities can be calculated for events such as tossing a coin, rolling a die or picking ball from a bag without looking.
Examples
1. Tossing a coin and landing on heads:
There are two possibilities, so the probability is 21=0.5=50%
2. Rolling a die and landing on 1,2,3,4,5 or 6:
There are six possibilities, so the probability is 61=0.16˙=16.6˙%
3. Spinning a 5-sided spinner and landing on side A, B, C, D or E:
There are five possibilities, so the probability is 51=0.2=20%
4. Picking a red marble from a marble bag with 30 marbles, 10 of each colour (red, green and blue):
There are three possibilities, so the probability is 31=0.33˙=33.3˙%