Probability Chapter 4

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Addition Rule: The addition rule for probabilities is used to determine the probability that at least one of the two events will occur. For example, for two events A and B, the addition rule can be used to determine the probability that either A or B will occur.

The addition rule can be specified as the probability of A, plus the probability of B, minus the joint probability of A and B. We subtract joint probability of A and B to avoid the double counting of common events.

Prob_Add_111

Prob_Add_112

Mutually Exclusive Events: If two events are mutually exclusive i.e. two events are disjoint and cannot occur together then:

Prob_Add_113

In that case, the probability that either A or B will occur is simply the sum of the unconditional probabilities for each event i.e.

Prob_Add_114

The Total Probability Rule: The total probability rule highlights the relationship between unconditional and conditional probabilities of mutually exclusive and exhaustive events. It is used to explain the unconditional probability of an event in terms of probabilities that are conditional upon other events.

In general, the unconditional probability of event R, is given by the following equation.

Prob_Add_115

where the set of events {Sl’ S2, • • • SN} is mutually exclusive and exhaustive.

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