4.3 Independence & Causality | 4.3 Independence & Causality | Unit 4: Probability | Mathematics for Computer Science | Electrical Engineering and Computer Science

<Mutually Independent Dice Rolls
4.3.1Independence: Video
4.3.2Independent Dice Rolls
4.3.3Mutual Independence: Video
4.3.4Mutually Independent Dice Rolls
4.3.5Independent vs Disjoint
4.3.6Labeled Balls
4.3.7Paradox
>Labeled Balls

Independent vs. Disjoint

Can two events be both disjoint and independent?

Never

Only if the two terms are equivalent

Only if the disjoint events are always independent

Only if at least one event is empty

Only if both events have are empty

Only if at least one event has probability 1 or is empty

Only if both events have probability 1 or is empty

Always

Events \(A\) and \(B\) are disjoint if \(A\cap B=\emptyset\) and they are independent if \(\Pr[A\cap B]=\Pr[A]\Pr[B]\). If \(A\cap B=\emptyset\), then since \(\Pr[\emptyset]=0\), we need either \(\Pr[A]=0\) or \(\Pr[B]=0\) for them to be independent as well.