# Is this true in probability? P(AUB)' = (P(A) + P(B)) '

• huan.conchito
In summary, the conversation is about probability and the formula for manipulating the expression P(A ∪ B). The question is whether P(AUB)' = (P(A) + P(B)) ' and the answer is yes, as long as A and B do not occur simultaneously. The formula for manipulating the expression when they do occur simultaneously is given as P{A ∪ B} = P{A} + P{B} - P{A ∩ B}.
huan.conchito

is this true in probability? P(AUB)' = (P(A) + P(B)) '

The question is
a) Assume that P(A) = 0.4 P(AnB)=0.1 P(A'nB')=0.2
P(B) = ?
what i did is:
P(AUB)= P(A)+P(B)- P(AnB)
P(AUB)= 0.4 + P(B)-0.1
P(A'nB')= 0.2 = P(AUB)' = 0.2 = 1 - (0.4 + P(B)-0.1)
P(B)= -0.5

NVM I GOT IT MYSELF

Last edited:
Only if A and B don't occur at the same time (simultaneously)

marlon

what is the formula to manipulate such an expression if they occur at the same time?

huan.conchito said:
is this true in probability? P(AUB)' = (P(A) + P(B)) '
Here is the general form:
P{A ∪ B} = P{A} + P{B} - P{A ∩ B}

~~

## 1. What does "P(AUB)" mean in probability?

In probability, "P(AUB)" represents the probability of event A or event B occurring, or the probability of the union of events A and B.

## 2. What is the formula for calculating "P(AUB)" in probability?

The formula for calculating "P(AUB)" is P(A) + P(B) - P(A∩B), where P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring together.

## 3. How is "P(AUB)" related to "P(A) + P(B)" in probability?

"P(AUB)" is related to "P(A) + P(B)" in probability because it represents the sum of the individual probabilities of event A and event B occurring. However, it also takes into account any overlap or intersection between the two events.

## 4. Is "P(AUB)" always equal to "P(A) + P(B)" in probability?

No, "P(AUB)" is not always equal to "P(A) + P(B)" in probability. It is only equal when the two events, A and B, are mutually exclusive, meaning they cannot occur at the same time. Otherwise, the formula for "P(AUB)" must include the subtracted probability of the intersection of events A and B.

## 5. Does the formula for "P(AUB)" apply to more than two events in probability?

Yes, the formula for "P(AUB)" can be extended to more than two events in probability. It becomes P(A) + P(B) + P(C) - P(A∩B) - P(A∩C) - P(B∩C) + P(A∩B∩C), where P(A∩B∩C) represents the probability of all three events occurring together.

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