## anonymous one year ago Consider the following scenario: • Let P(C) = 0.2 • Let P(D) = 0.3 • Let P(C | D) = 0.4 Find P(D | C) Find P(C AND D).

1. anonymous

First you want to find C and D, which is the same as D and C

2. anonymous

$\Pr(C|D ) = \frac{\Pr(\underbrace{C\cap D}_{C\text{ and } D})}{\Pr(D)}$

3. anonymous

This equation gets manipulated into: $\Pr(C|D)\cdot \Pr(D) = \Pr(C\cap D)$

4. anonymous

wait so "|" is the same as saying "and?"

5. anonymous

No, $\Pr(\underbrace{C|D}_{C\text{ if/given }D})$

6. anonymous

oh okay right

7. anonymous

so it would be 0.12?

8. triciaal

|dw:1436240223932:dw|

9. triciaal

|dw:1436240600971:dw|

10. anonymous

Yes, $$0.12$$ works for C and D

11. anonymous

Divide that by $$\Pr(C)$$ to get $$\Pr(D|C)$$.

12. misty1212

$P(C|D)=\frac{P(C\cap D)}{P(D)}=\frac{P(C\cap D)}{.3}=.4\to P(C\cap D)=03\times .4=.12$

13. misty1212

then $P(D|C)=\frac{P(C\cap D)}{P(C)}=\frac{.12}{.2}$

14. anonymous

oh cool makes sense thanks