Answer to Question #350810 in Statistics and Probability for Roe

Question

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

Answer 1

Solution:

$P(A/B)-$ 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:

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

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. $A∩B=∅; \space P(A∩B)=0.$ Because, when B occurred, A can not occurred.