Probability
- Probability involves the study of the laws of chance and is a measure of the likelihood of an event happening.
- Rather than use words to describe the chance of an event happening, we can give probability as a number, usually written as a fraction or decimal, between 0 and 1.
- If it is impossible for an event to happen then the probability is 0.
- If an event is certain to happen then the probability is 1.
- All other probabilities are greater than 0 but less than 1.
- Sometimes probabilities are written as percentages, between 0 and 100%.
- To compare probabilities you must compare the relative sizes of the fractions, decimals or percentages.
Listing Outcomes
- Consider a six sided die, on one throw of the die you can have 1 of 6 possible outcomes i.e. 1,2,3,4,5,6.
- If you want to find the event “The number on the die is an even number” then you would be interested in the numbers 2,4,6 . These numbers are said to be favourable outcomes.
Calculating Probabilities
- If, in an experiment each outcome is as likely to occur as any other outcome then you have what are called equally likely outcomes.
- It is possible to calculate the probability of an event happening using the following formula:
Probability of an event happening = (Number of favourable outcomes) / (Total number of outcomes)
When it comes to IGCSE/GCSE Maths, do you remember how to calculate the probability of the two main types of events?
Mutually Exclusive Events
Mutually exclusive events are events which cannot happen at the same time.
If you roll a die the outcome will be a score of 1,2,3,4,5,6 but only one of these can occur, for example, the score 2 and 3 cannot occur at the same time.
For any two mutually exclusive events A and B:
P(A or B) = P(A)+P(B)
The probability of an event not happening can be expressed thus: P(event does not happen) = 1- P(event happens)
Independent Events
- Independent events are events, which do not affect each other e.g. tossing a coin and throwing a die.
To find the probability that two independent events will happen we multiply their respective probabilities:
P(A and B) = P(A) * P(B)
Tree Diagrams
- Listing outcomes can be a very hazardous job.
- A tree diagram is another way of listing outcomes and helps to simplify the calculation of probabilities when combined events are concerned.
- Each ‘branch’ of the tree indicates the outcome at each stage.
- Each route along the tree leads to a combined event.
- The tree is usually created across the page but can be drawn down the page.
- Consider a coin being tossed three times, the diagram below represents the possible outcomes, where H denotes a head and T a tail.
That's the end of the topic!
Drafted by Bonnie (Mathematics)