Question

We are told that events A and B are conditionally independent, given a third event C, and that P(B∣C)>0. For each one of the following statements, decide whether the statement is “Always true", or “Not always true."

A and B are conditionally independent, given the event Cc.

- unanswered

A and Bc are conditionally independent, given the event C.
- unanswered

P(A∣B∩C)=P(A∣B)
- unanswered

P(A∣B∩C)=P(A∣C)

Answer 1

1. Not always true

2. Always true

3. Not always true

4. Always true

(I am taking this exam, too)