Hello, anthmoo!

Given: .P(A) = 13/25, .P(B) = 9/25, .P(A|B)= 5/9

Determine the probabilties:.

a) P(A U B) . . b) P(A'|B') . . c) P(A U B')

I would use Bayes' Theorem, then draw a Venn diagram.

. . . . . . . . . . . . . . . P(A ∩ B)

We have: .P(A|B) .= .---------- .= .5/9

. . . . . . . . . . . . . . . . . P(B)

. . . . . . . . . . . . . . . . . . . . .P( A ∩ B)

Since P(B) = 9/25, we have: .----------- .= .5/9

. . . . . . . . . . . . . . . . . . . . . .9/25

. . Hence: .P(A ∩ B) .= .1/5

Now we can draw the Venn diagram.

Code:

*---------------------------------------------------*
| |
| *-----------------------* |
| | A | |
| | 8/25 | |
| | | |
| *-----------+-----------* | |
| | | | | |
| | | 1/5 | | |
| | | | | |
| | *-----------*-----------* |
| | | |
| | 4/25 | |
| | B | |
| *-----------------------* 8/25 |
| |
*---------------------------------------------------*

You should be able to answer the questions now.