Discussion Overview
The discussion revolves around proving the relationship p(A|B') = p(A|B) within the context of probability theory, specifically focusing on the conditions under which this relationship holds, particularly in relation to independent events.
Discussion Character
- Technical explanation, Debate/contested
Main Points Raised
- One participant attempts to derive the relationship using the definitions of conditional probability but expresses uncertainty about the validity of their solution.
- Another participant asserts that the relationship p(A|B') = p(A|B) cannot be proven in general and is only true for independent events.
- A later reply clarifies that if A and B are independent, then by definition, p(A|B) equals p(A), which implies p(A|B') also equals p(A).
Areas of Agreement / Disagreement
There is a disagreement regarding the generality of the relationship. Some participants agree that it holds under the condition of independence, while the initial claim suggests uncertainty about the proof without that condition.
Contextual Notes
The discussion highlights the dependency on the assumption of independence between events A and B, which is crucial for the relationship to hold. There are also unresolved steps in the initial proof attempt.