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

• Mdhiggenz
In summary, P(AB) represents the probability of the intersection of events A and B, P(AB)c represents the probability of the complement of the intersection of events A and B, and P(A∪Bc) represents the probability of the union of event A and the complement of event B. The complement of B is everything that is not in B, and has no relation to event A.
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∪Bc)
Means all the sets not including B

Mdhiggenz said:

## 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∪Bc)
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?

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

Mdhiggenz said:
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.

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?

Mdhiggenz said:
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.

## 1. What does P(AB) mean in a union definition?

P(AB) in a union definition means the probability of both events A and B occurring at the same time.

## 2. How is P(AB) calculated?

P(AB) is calculated by dividing the number of outcomes where both events A and B occur by the total number of possible outcomes.

## 3. What is the significance of P(AB) in a union definition?

P(AB) is important in a union definition because it helps us understand the likelihood of two events occurring together, which can help in decision making and predicting outcomes.

## 4. What does P(AB)c mean in a union definition?

P(AB)c in a union definition means the probability of the complement of event AB, which is the probability of one or both events A and B not occurring.

## 5. How is P(AB)c related to P(AB) in a union definition?

P(AB)c is the complement of P(AB), meaning that P(AB)c + P(AB) = 1. This relationship helps us understand the probability of all possible outcomes in a union.

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