Three Concepts: Probability | Projects
The lecturer (Petri) reveals that one of the Three Concepts courses is better than the other two. You need to take just one course before graduation, and you would like to pick the best one. Luckily, Petri has promised to help you a little. After you have chosen one course — in this case, Probability — Petri reveals you that one of the remaining courses — say, Utility — is surely not worth taking. Should you now stick to Probability or switch to Information?
A Variant: Imagine that before Petri tells you which one of the courses is surely worthless, another student interrupts your conversation with Petri by demanding to know if a specific Three Concepts course — which happens to be one of the two you didn't choose — is worth taking. You know that your friend hasn't done any of the courses. Petri tells her that the course is useless. Should you now stick or switch?
Two eight-sided fair dice (faces numbered 1 to 8) are thrown repeatedly; the outcome of each throw is the sum of the numbers showing. Mr. C. Ray, who says that 8 and 10 are his lucky numbers, bets even money that an 8 will be thrown before the first 9 is thrown. If you were a gambler (hypothetically, of course), would you take the bet? What is your probability of winning? Mr. C. Ray then bets even money that a 10 will be thrown before the first 9 is thrown. Would you take the bet?
Having gained your confidence, Mr. C. Ray suggests combining the two bets into a single bet: he bets a larger sum, still at even odds, that an 8 and a 10 will be thrown before two 9s have been thrown. Would you take the bet? What is your probability of winning?
Challenge (not needed to get full points for the problem, but gives you extra fame :-): What is the probability that you win on the nth roll?
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| Three Concepts: Probability | |