4.3 Independence & Causality


Suppose event A is evidence that event H occurred, and event B is also evidence that H occurred. Is (A or B) necessarily evidence that H occurred? A precise way of thinking about evidence is that E is evidence for H if \(\Pr[H|E]>\Pr[H]\).

Exercise 1

Consider the following counterexample: Suppose we roll a standard fair 6-sided die. Define the following events: \[H:=\text{Die lands 3 or 4}\]\[A:=\text{Die lands 4 or less}\]\[B:=\text{Die lands 3 or greater}\] Clearly A is evidence for H, and B is evidence for H, but (A or B) is not evidence for H.