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 *-----------------------* |
| |
*-----------------------------------------------*