Notes > Foundations of Computing > Probability
The "chance" or "likelihood" of events happening refers to the probability of the event happening. Probabilities can be represented numerically in different ways as listed below:
An "outcome" is a single possible result that can occur from an experiment or test. An "event" is an outcome that we are specifically interested in. The "sample space" is the set of all possible outcomes. For example, when tossing 2 coins, the sample space is (HH,HT,TH,TT) where "H" represents getting a head and "T" represents getting a tail.
- Percentage chance - where the probability is stated as a percentage (e.g. 70%). A percentage chance can also be written in the form of a ratio (e.g. 70:30).
- Ratio chance - where the probability is written as "one in x" where x is a whole number (e.g. "1 in 2" - represents a 50% percentage chance)
- Probability - where a fraction or decimal number is used to represent the chance of an event occuring (e.g. "0.5" or "1/2"). A probability of "1" therefore means that the event will definitely occur.
The "total law of probability" describes the fact that the sum of the probabilities of every possible outcome in an experiment equals 1.
Conditional probability involves the calculation of the probability of an event given that another event has occurred. This is only applicable to events which are dependent. For example, drawing cards from a pack of cards and not replacing them will mean that the probability of the second card being drawn will be affected by the first card that is drawn.
Venn Diagrams can be used to represent a sample space and the possible events that can occur within it. Circles within a Venn Diagram represent event spaces. If these event spaces overlap then the events are not mutually exclusive. Completely separate event spaces show that the events are mutually exclusive (i.e. if one occurs, the other cannot occur). Mutually exclusive events can be described as "complementary" or opposite events. Mutually exclusive events cover all the possible outcomes for a test. If a certain event occurs, it is important to note that its complementary event cannot occur.
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