Calculations involving Venn diagrams use the formulae:
and if the events
and
are 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.
If
andare independent,
– the probability that A happens but not
and
– the probability that happens but not
Example: A and B are independent.
Sketch the Venn diagram.
andare independent
Example:and
are independent.
and
Sketch a possible Venn diagram.
Use
and
to obtain
(1)and
(2). We have to solve these simultaneous equations inand
rearrange (1) to give
and substitute this into (2) to get
Rearrangement of this equation gives
Solving this quadratic equation gives
or 0.8702. If
