- #1
zeion
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Homework Statement
I need to expand this:
P(A∪B∪C∪D)
A,B,C,D are not disjoint.
Homework Equations
The Attempt at a Solution
P(A∪B∪C∪D) = P(A) + P(B) + P(C) + P(D) - P(A∩B) - P(A∩C) - P(B∩D) - P(C∩D) + P(A∩B∩C∩D)
Is that right
zeion said:Homework Statement
I need to expand this:
P(A∪B∪C∪D)
A,B,C,D are not disjoint.
P(A∪B∪C∪D) = P(A) + P(B) + P(C) + P(D) - P(A∩B) - P(A∩C) - P(B∩D) - P(C∩D) + P(A∩B∩C∩D)
Is that right
zeion said:I don't get it. Those weird symbols are confusing.
So is it
P(A∪B∪C∪D) = P(A) + P(B) + P(C) + P(D) - P(A∩B) - P(A∩C) - P(A∩D) - P(B∩C) - P(B∩D) - P(C∩D) + P(A∩B∩C) + P(A∩B∩D) + P(B∩C∩D) + P(A∩B∩C∩D) ?
zeion said:So I minus the last term because I'm adding 4 things?
If it's 3 things I add?
LCKurtz said:Yes. The signs alternate in that fashion.
zeion said:why?
zeion said:wow that's so annoying.
so if I had like 20 terms it's hard to do by hand
eldani said:Since they're independent,
P(A∪B∪C∪D) = P(A) + P(B) + P(C) + P(D)
The probability union thing refers to the combination of events in probability theory. It represents the likelihood of two or more events occurring together.
To calculate the probability union, you need to add the individual probabilities of each event and subtract the probability of their intersection. The formula is P(A∪B) = P(A) + P(B) - P(A∩B).
No, the probability union can never be greater than 1. This is because the sum of probabilities can never exceed 1, which represents 100% certainty.
The probability union represents the likelihood of either of the events occurring, while the probability intersection represents the likelihood of both events occurring simultaneously.
The probability union is important in statistics as it allows us to calculate the likelihood of multiple events happening at the same time. It is used in various statistical analyses, such as hypothesis testing and decision making.