1. ## 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

2. $\displaystyle P(B\cap C) = P(B)P(C)=.2P(C)$ (by indeoendence)

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

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

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

$\displaystyle .24= .8P(C)$

$\displaystyle P(C)=.3$

3. Hello, wahhdoe!

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

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

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

DrSteve did an excellent job!

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

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

The Venn diagram looks like this:

Code:

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