STT 212 Lecture Notes - Lecture 10: Sampling Distribution, Conditional Probability, Sample Space
28 May 2017
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Addition rule: p(a or b) = p(a) + p(b) - p(a and b) Double count middle part so must subtract middle part. *with disjoint events, the p(aorb) = p(a) + p(b: don"t share events. Easier with disjoint: conditional probability, p(a|b) = probability of a given b, given that event b has occurred, what is the probability that event a will occur. A [1,2,3}, b{2,4,6: 1/3, make sample space smaller, p(a and b) / p(b, multiplication rule, p(a and b) = p(a|b) p(b, ex: stack of 4 cards, 2 red, 2 black. Select 2 cards, one at a time, do not replace 1st card before selecting 2nd card. 2/4 x 1/3 = 1/6: make a tree diagram! Independent events: a and b are statistically independent events if p(a|b) = p(a, ex: Roll a die, let a = {1,2,3}, b={1,3,5} No because p(a|b) = 2/3 and p(a) = 3/6. If (p and b) does not equal p(a)xp(b), are independent.
