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Explain why P(AorB)P(A)+P(B). Then use the general addition rule to findP(AorB).

Short Answer

Expert verified

The likelihood of P(AorB)P(A)+P(B)and the occurrence A or B

Step by step solution

01

Step 1. Given Information    

P(AorB)P(AB)P(AorB)P(A)+P(B)

02

Step 2. Concept Used   

Definition of the probability addition theorem: Assume Aand Bare two events in a random experiment, and you want to know whether Aor Bhas a higher likelihood. Then apply the probability addition theorem.

03

Step 3. Calculation    

let A and B be two events of a random experiment using the addition theorem of probability. That isP(AorB)=P(AB)P(AorB)=P(A)+P(B)P(AB)

If A and B are not mutually exclusive events. So, P(AB)0P(AorB)P(A)+P(B)

Therefore, The event and the probability of P(AorB)P(A)+P(B)

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