Conditional Probability

Probability of a second event occurring given that a first event has already happened. Requires that one of these events is a Dependent Event

This may lead to the Sample Space for the second event to be smaller or bigger than the sample space of the first event. $P(E|F)=\frac{P(E\cap F)}{P(F)}$ OR $P(A\cap B)=P(A|B)\ast P(B)=P(B|A)\ast P(A)$

Example

1% of people in lost articles realized theyve been punked. 5% of all people are in lost articles. What are chances that a person at lost articles will realize they’ve been punked? P(A) = 5% P(B|A) = 1% P(A|B) = 0.2