MATH 141 Lecture Notes - Lecture 9: Conditional Probability

• School: Bloomsburg University
• Department: Mathematics
• Course: MATH 141
• Professor: Zhang

Document Summary

Conditional probability and its application case difference. Let say we have events a and b. If the result of event a does not influence the result of event b, we say these events are independent. If event a and b are independent, because we need to get event a done first step and b for the second step. What is the pro(cid:271)a(cid:271)ility of o(cid:271)tai(cid:374)i(cid:374)g a (cid:858)(cid:1006)(cid:859) = (cid:1005)/6. Based on an event b in the past (reason event: you know my number is even) to fore(cid:272)ast the e(cid:448)e(cid:374)t a (cid:894)o(cid:271)tai(cid:374)i(cid:374)g a (cid:858)(cid:1006)(cid:859)(cid:895) i(cid:374) the future. A|b: the conditional event a, given the reason event b has already happened. P(a|b): the probability that a happens given the result of b. Independence: two events a and b, if the results do not influence each other. Dependence: consider different results of b, the probability of a will be changed. A and b are independent p(a|b) = p(a) p(a and b) = p(a) p(b)