Druyd:Knowledge

Multiple Events

Storyboard

When there are multiple events, there are different probabilities of occurrence of combinations of these, to the extent that they are exclusive or not. On the other hand, there are situations in which events condition other events and are key to studying developments when what happens in the future depends on what happened today.

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Case Multiple Events

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Independent Events

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Probability of Independent Events

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$P(A\cap B)=P(A)P(B)$

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Events mutually Exclusionary

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In the event that the events are mutually exclusive, if A does not occur, B and if B does not occur, A.

In this case the probability that both occur simultaneously is zero. Thus

$ A \cap B = \emptyset $

The probability of A or B occurring corresponds to each outcome that one or the other produces. This corresponds to the union of both A \cup B events and is calculated by adding both probabilities.

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Probabilities of mutually exclusive Events

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$P(A\cup B)=P(A)+P(B)$

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Sets without Common Elements

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Events not mutually exclusive

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Sets with Intersection

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Not mutually exclusive representation of Events

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If the events are NOT mutually exclusive, the sets can have points in common, that is, their intersection is NOT empty

$ A \cap B \neq \emptyset $

If you want to calculate the probability that A or B will occur as the sum, you will have the problem that the area of the intersection will be counted twice. Therefore, it is necessary to subtract once the area of the intersection in order to have the total number of events in a unique way.

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Probability of NON Independent Events

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When the events A and B are NOT mutually exclusive, the probability is calculated as the sum of the P(A) probabilities that will occur A and P(B) occur B, there being the problem that the set A \cap B in which they can coincide, would be adding twice. Therefore the probability is the sum minus the probability that they coincide:

$P(A \cup B)=P(A)+P(B)-P(A \cap B)$

The sum never exceeds unity since both sets do not intercept and the sum cannot be greater than all possible cases.

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