What do P(A'uB) and P(AuB') mean in probability notation?

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repugno
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Hello everyone, I feel ashamed to be asking someone to explain such simple notation to me, but I’m having serious problems understanding it. Any help would be deeply appreciated. Thank you.

I’ll use “u” and “n” to denote Union and Intercept as I don’t know how to make the symbols.

What I can understand of the notation is as follow.

If A and B are two events and P(A) = 0.6, P(B) = 0.3 and P(AuB) = 0.8

P(A) would be the probability of event A occurring by itself and
P(B) would be the probability of B occurring by itself.
P(AuB) would be either A or B occurring.
P(AnB) would be when A and B occurs at the same time.
P(A’) when A does not occur, so 1 – P(A)
P(B’) when B does not occur, so 1 – P(B)

Now the confusing part…

P(A’nB) What I can understand from the “n” notation is that it represents events happening at the same time, so this would be when A does not occur at all but B does.

What would P(A’uB), P(AuB’) be ?? I’m very confused now. :frown:
 

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P(A'∩B) is when A doesn't occur and B does occur.

P(A∩B') is when A does occur and B doesn't occur.

P(A'∩B) = P(AUB) - P(A)

edited to add: I don't seem to have the union in my chracter set. Also, the union and intersection symbols are "& cup ;" and "& cap ;" respectively (both without the spaces), you won't be able to display them unless they are on your html chracter set though.
 
Last edited:
Thanks for the reply.

What would this notation represent?

P(A'∪B)
P(A∪B')
 
P(A'UB) represents either B or not A = 1 - (P(A)-P(A∩B))

p(AUB') represents either A or not B