## 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.

andare independent

Example:andare independent.andSketch a possible Venn diagram.

Useandto obtain

(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