STA 2023 Lecture Notes - Lecture 11: Mutual Exclusivity, Sample Space, Vehicle Insurance
Document Summary
Conditional probability that event a occurs given that event b has occurred. Define: a = get an odd number {1, 3, 5, b = get a number greater than or equal to 4 {4, 5, 6, sample space = 1, 2, 3, 4, 5, 6, conditional sample space: If you are told that even a happen, then the conditional sample space is 1, 3, and 5. If you know b has occurred, the sample space has been reduced to 4, 5, and 6. Thus the conditional probability of event a is 1/3. P ( a|b ) (cid:862)the p(cid:396)o(cid:271)a(cid:271)ility a o(cid:272)(cid:272)u(cid:396)s given b has o(cid:272)(cid:272)u(cid:396)(cid:396)ed(cid:863) P ( a|b ) = (cid:4666) (cid:3002) (cid:3003) (cid:4667) (cid:4666)(cid:3003)(cid:4667) (cid:2869)/(cid:2874)(cid:2871)/(cid:2874)=1/3. Psychologists tend to believe that there is a relationship between aggressive behavior and order of birth. To test this belief, a psychologist chose 500 elementary school students at random and administered ea(cid:272)h a test desig(cid:374)ed to (cid:373)easu(cid:396)e the stude(cid:374)t"s agg(cid:396)essi(cid:448)e(cid:374)ess.
