# 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 $$\Pr[H|E]>\Pr[H]$$.
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.