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A compound event is any event combining two or more simple events.

The notation for addition rule is: P(A or B) = P(event A occurs or event B occurs or they both occur).

When finding the probability that event A occurs or event B occurs, find the total numbers of ways A can occurs and the number of ways B can occurs, but find the total in such a way that no outcome is counted more than once.

General addition rule is :

P(A or B) = P(A) + P(B) - P(A and B), where P(A and B) denotes that A and B both occur at the same time as an outcome in a trial procedure.

It is a special addition rule that shows that A and B cannot both occur together, so P(A and B) becomes 0:

If A and B are mutually exclusive, then P(A) or P(B)= P(A or B) = P(A) + P(B)

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Q: What is the Addition Theorem in probability?
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How can you state and illustrate the addition multiplication Theorem of Probability?

Addition Theorem The addition rule is a result used to determine the probability that event A or event B occurs or both occur. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A or event B occurs : = probability that event A and event B both occur ; For mutually exclusive events, that is events which cannot occur together: : = 0 ; The addition rule therefore reduces to : = P(A) + P(B) ; For independent events, that is events which have no influence on each other: : ; The addition rule therefore reduces to : ; Example ; Suppose we wish to find the probability of drawing either a king or a spade in a single draw from a pack of 52 playing cards. ; We define the events A = 'draw a king' and B = 'draw a spade' ; Since there are 4 kings in the pack and 13 spades, but 1 card is both a king and a spade, we have: : = 4/52 + 13/52 - 1/52 = 16/52 ; So, the probability of drawing either a king or a spade is 16/52 (= 4/13).MultiplicationTheorem The multiplication rule is a result used to determine the probability that two events, A and B, both occur. The multiplication rule follows from the definition of conditional probability. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A and event B occur : P(A | B) = the conditional probability that event A occurs given that event B has occurred already : P(B | A) = the conditional probability that event B occurs given that event A has occurred already ; For independent events, that is events which have no influence on one another, the rule simplifies to: : ; That is, the probability of the joint events A and B is equal to the product of the individual probabilities for the two events.


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The addition rule is used when calculating the probability of two mutually exclusive events occurring together. For example, when calculating the probability of rolling a 2 or a 6 on a six-sided die, you would use the addition rule.


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