Re: Number of Essay questions that I have to do.
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If there are 6 possible essay questions, 2 will be chosen at random to be on a test, and I have to pick 1 of them to write, how many of them should I prepare for beforehand to ensure an 80% chance that one of the ones that I prepare for will be on the test?
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You need to prepare 3. There are C(6,2) = 6*5/2 = 15 possible tests. If you prepare 3 essays, there will only be C(3,2) = 3*2/2 = 3 tests which use only the 3 that you didn't prepare, and this is 3/15 = 1/5 or 20% of the tests. So 4/5 or 80% will have at least one of the essays you prepared.
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