# Venn Diagrams

• Dec 12th 2010, 09:27 AM
wahhdoe
Venn Diagrams

Q) Create a venn diagram using this information: P(A)=0.4, P(B)=0.2, P(AnC)=0.04, P(BuC)=0.44, B & C are independent and A & B are mutually exclusive.

if possible could someone please draw the venn diagram with an explanation

the main trouble im having is where to use the fact that B & C are independent.

thanks
• Dec 12th 2010, 10:21 AM
DrSteve
$P(B\cap C) = P(B)P(C)=.2P(C)$ (by indeoendence)

$P(B\cup C) = P(B)+P(C)-P(B\cap C)$

$.44= .2+P(C)-.2P(C)$

$.44= .2+.8P(C)$

$.24= .8P(C)$

$P(C)=.3$
• Dec 12th 2010, 01:14 PM
Soroban
Hello, wahhdoe!

Quote:

$\text{Create a Venn diagram using this information:}$

. . $P(A)=0.4,\;P(B)=0.2,\;P(A \cap C)=0.04,\;P(B \cup C)=0.44$

. . $B\text{ and }C\text{ are independent, and }A\text{ and }B\text{ are mutually exclusive.}$

DrSteve did an excellent job!

He found that: . $P(C) = 0.3$

Since $\,B$ and $\,C$ are independent:
. . $P(B \cap C) \:=\: P(B)\cdot P(C) \:=\:(0.2)(0.3) \:=\:0.06$

The Venn diagram looks like this:

Code:

       *-----------------------------------------------*       |                                              |       |  *---------------*      *---------------*  |       |  | A            |      |            B |  |       |  |  0.36        |      |        0.14  |  |       |  |              |      |              |  |       |  |      *-------+-------+-------*      |  |       |  |      |  0.04 |      |  0.06 |      |  |       |  |      |      |      |      |      |  |       |  *-------+-------*      *-------+-------*  |       |          |          0.2          |          |       |          |          C          |          |       |  0.2    *-----------------------*          |       |                                              |       *-----------------------------------------------*