Venn Diagrams 2
Calculations involving Venn diagrams use the formulae:
and if the eventsandare independent,where for example, P(A) indicates the probability of A happening.
The best way to illustrate the use of these examples is by way of examples. A Venn diagram can be solved completely with three conditions.
Example:andare independent. Sketch the Venn diagram.
Ifandare independent,– the probability that A happens but notand– the probability that happens but not
Example: A and B are independent.Sketch the Venn diagram.
Example:andare independent.andSketch a possible Venn diagram.
(1)and(2). We have to solve these simultaneous equations inand
rearrange (1) to giveand substitute this into (2) to get
Rearrangement of this equation gives
Solving this quadratic equation givesor 0.8702. If