Question #350810

Prove that the probability of P(A/B)=0

1
Expert's answer
2022-06-15T18:02:26-0400

Solution:

P(A/B)P(A/B)- called condition probability;

If A and B are two events in a sample space S, then the conditional probability of A

A given B is defined as:

P(A/B)=P(AB)P(B);P(A/B)=\frac{P(A∩B)}{P(B)}; when P(B)0;P(B)\ne0;

When A and B are disjoint they can not both occur at the same time. Thus, given that B has occurred, the probability of A must be zero. AB=; P(AB)=0.A∩B=∅; \space P(A∩B)=0. Because, when B occurred, A can not occurred.



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