Re: mutual exclusivity
[ QUOTE ]
p(A) is indeed .5 and p(B) is indeed .35
I can't get my head around the 0.05 answer, it just doesn't add up for me, I'm probably wrong but heres why I think its not 0.05:
[/ QUOTE ]
I guarantee you're wrong; didn't you see my proof? What step don't you agree with? The three numbers you are given add up perfectly to
P(A) + P(B) + P(A' and B') = 1 + P(A and B).
Think about it. If you count everything in set A, plus everything in set B, plus everything in neither, then you have counted everything with the stuff in both A and B counted twice. I spelled out the proof of this, which just comes from this fundamental relation which you have to know:
P(A or B) = P(A) + P(B) - P(A and B).
This is always true. If A and B were mutually exclusive, then P(A and B) = 0, by definition. Mutual exclusivity means that both A and B cannot both happen.
[ QUOTE ]
In a perfect world probability AB = .5 * .35 = .175
if we take the chance of them both not happening in a perfect world it is .5 * .65 = .325
[/ QUOTE ]
This is only true when A and B are independent. If they were mutually exclusive, then P(A and B) = 0.
[ QUOTE ]
So if the probability of them both not happening goes down then doesn't it follow logic that the chance that both of them happen goes up?
[/ QUOTE ]
Of course not. It just means that the chance that one of them happens goes up. If the chance of A and B remain the same while the chance of them both not happening goes down, then the chance of them both happening must also go down.
If you can't see it, draw a Venn diagram, with 2 overlapping circles inside a box. As you move the two circles apart, the area outside the circles gets smaller. This is A' and B'. Also, the area of overlap gets smaller. This is A and B. The area inside the circles goes up. This is A or B.
[ QUOTE ]
I don't see why the probability of both of them happening goes from .175 to .05. The additional .125 of mutual unexclusivity needs to be added somewhere, I don't see how it works against P(AB).
[/ QUOTE ]
Again, you are confusing independence and mutual exclusivity. The "extra .125" is for the case where A and B are independent, not mutually exclusive. Compared to mutual exclusivity, P(AB) increased from 0 to 0.05.
|