Question

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).

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

oh okay right

Answer 7

so it would be 0.12?