Probability from Venn Diagrams

A Venn diagram visualises the relationship between different sets or groups of data. Circles or other shapes represent sets, with shared regions showing where the sets overlap (indicating shared characteristics).
Probability is the measure of the likelihood that an event will occur in a random experiment. It’s calculated as the number of favourable outcomes divided by the total number of possible outcomes.
The Principle of Addition can be applied to events within a Venn Diagram. This means that the probability of either of two mutually exclusive events occurring is the sum of the probabilities of both events.
If the events are not mutually exclusive (i.e., they can occur at the same time), then the Principle of Addition must be adjusted to subtract the probability of both events occurring: P(A or B) = P(A) + P(B) - P(A and B).
The Principle of Multiplication is also applicable. This refers to the probability of two independent events occurring sequentially: P(A then B) = P(A) * P(B). However, if the events are not independent, you must adjust for the probability of the first event affecting the second: P(A then B) = P(A) * P(B given A).
For problems involving conditional probability: If the probability of an event B is affected by the occurrence of event A, then P(B given A) — the probability of event B given A has occurred — can be found using a Venn diagram.
Each point within a circle of a Venn diagram represents an element in a set. To find the probability of an event, determine how many points represent the event outcome and divide that by the total number of points.
To calculate probabilities from a Venn diagram, you should write the probabilities inside the relevant parts of the Venn diagram, and you could also add probabilities up across the whole probability space to make sure that they add up to 1 as they should.
Understanding Venn diagrams can aid in understanding the concepts of union, intersection and complement of sets. These are key concepts in probability theory.
Sample space, a key term in probability, denotes the set of all possible outcomes of an experiment. A Venn diagram can be used to illustrate the sample space.