Union Definition: P(AB) and P(AB)c Explained

[Mdhiggenz]

Homework Statement

Can you guys explain to me what the following mean.

We are working on probability and unions, and these came up on the homework and need to know what these mean in order to solve the problem.

Thanks

P(AB)

P(AB)^c

Where c is the compliment.

Also i want to make sure I have the following definitions correct.

P(A∪B^c)
Means all the sets not including B

Homework Equations

The Attempt at a Solution

 

[LCKurtz]

Homework Statement

Can you guys explain to me what the following mean.

We are working on probability and unions, and these came up on the homework and need to know what these mean in order to solve the problem.

Thanks

P(AB)

Likely the probability of $A\cap B$

P(AB)^c

Where c is the compliment.

That's spelled complement. I would say that need another set of parentheses and I'm guessing it means the probability of $(A\cap B)^c$

Also i want to make sure I have the following definitions correct.

P(A∪B^c)
Means all the sets not including B

It is a probability, not a set or a point. But what about a point that is in A and in B?

 

[Mdhiggenz]

Thanks for the response, wouldn't a set in A and in B still have B in it, so be irrelevant?

 

[LCKurtz]

Thanks for the response, wouldn't a set in A and in B still have B in it, so be irrelevant?

It doesn't make sense to talk about "set in A and in B". A and B are sets. They have elements or members, or, informally, in the case of Venn diagrams, points in them. The notation shows the complement on B. But a point in A is in that union whether or not it is also in B.

 

[Mdhiggenz]

so when they say B complement, it simply means calculate everything except the section that is "pure" B. Such as include the ones that are neither A or B?

 

[LCKurtz]

so when they say B complement, it simply means calculate everything except the section that is "pure" B. Such as include the ones that are neither A or B?

Yes, the complement of B is everything that is not in B. It, itself, has nothing to do with A.