and
if the events
and
are
independent,
where
for example, P(A) indicates the probability of A happening.
A Level Maths Notes: S1 – 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.
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
