Hi, this is a question from a probability course:

STATE TRUE OR FALSE

LetA,B , andC

be events associated with the same probabilistic model (i.e., subsets of a common sample space), and assume thatP(C)>0

.

For each one of the following statements, decide whether the statement is True (always true), or False (not always true).

1. Suppose thatAC . Then,P(AC)P(A)
2. Suppose thatAB . Then,P(AC)P(BC)
3. Suppose thatP(A)P(B) . Then,P(AC)P(BC)
4. Suppose thatAC,BC, andP(A)P(B). Then,P(AC)P(BC).

Additional question, what if C is not independent for cases 2, 3 and 4. Let's assume That B = {1,2,3,4} A={1,2} and C={1,2,5,6,7} wouldn't P(A|C) be higher that P(B|C)? Thanks for your clarification.