Events $E$ and $F$ are such that $P(\text{not } E \text{ and not } F) = 0.25$. State whether $E$ and $F$ are mutually exclusive.
(N/A) It is given that $P(\text{not } E \text{ or not } F) = 0.25$.
By De Morgan's Law,this is equivalent to $P((E \cap F)') = 0.25$.
We know that $P(E \cap F) = 1 - P((E \cap F)')$.
Substituting the value,we get $P(E \cap F) = 1 - 0.25 = 0.75$.
Since $P(E \cap F) = 0.75 \neq 0$,the events $E$ and $F$ are not mutually exclusive.
By De Morgan's Law,this is equivalent to $P((E \cap F)') = 0.25$.
We know that $P(E \cap F) = 1 - P((E \cap F)')$.
Substituting the value,we get $P(E \cap F) = 1 - 0.25 = 0.75$.
Since $P(E \cap F) = 0.75 \neq 0$,the events $E$ and $F$ are not mutually exclusive.
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