Lecture 17 conditionalprobability• Example : SARS• Sample space, basic outcome, and event• Basic rule• A and B ( in both A and B) , A or B (in either A orB or both)• Conditional probability of B given A• =P{B|A}= P{A and B}/P{A}• Probability of death for China• Given a SARS death case, what is the probabilitythat the case is from China?• Class enrollment : by year and by major• Year : freshman, sophomore, junior, senior• Major, life science, social science, mathscience,•Class enrollment : by year and by major•Year : freshman, sophomore, junior, senior•Major, life science, social science, math science, •A=freshman, B=life science•A and B = life science freshman•P(A)=30%, P(B)=35%, P(A and B)=25%•Find P(non-life science freshman)•Randomly select a student. It turns out that he/she is not• a freshman. What is the probability that he/she majors in •life science?Prisoner’s dilemma• Three prisoners , A, B, C are in jail. One of themis to be executed and the other two will be set free.Prisoner A asked the guard : one of my partners Bor C will be set free. Could you please tell mewhich one of them will be set free?• Guard thought a while and told A : If I do not tellyou, then your chance of death is 1/3. But if I tellyou, then there are only two left and you are oneof them to be killed. Your chance of death will be1/2. Do you really want to increase your chance ofdeath ?•Drawers A and B•A has a good coin and a fakecoin•B has two good coins and afake coin•Open a drawer and pick a coin.•Chance of getting fake one.•Given the fake one is selected,what is the chance that it camefrom drawer
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