Probability Q: Explaining Union & Independent Events

[barksdalemc]

I am reviewing for a midterm and something I looked at before is confusing me. Can someone give me an explanation? If a sample space has events A1 A2, then the prob(A1 U A2)= prob (A1) + prob (A2) - prob (A1intA2). That makes perfect sense. If they are disjoint, then the union is just the sample space itself. Now if the events are independent of each other then the last term is the product of P(A1) and P(A2). But does this only refer to two separate events? In other words you can't really use the independence within a sample space right? Does it have to be two events like one flip of a coin and then another flip?

Thanks in advance

 

[lippyka]

. Yes, the independence only applies to two separate events. It does not refer to a sample space as it applies to two events independently of each other. For example, if you have a single coin flip, then you cannot apply the independence principle as there is only one event (the coin flip). However, if you have two coin flips, then you can apply the independence principle because each coin flip is an independent event.