I have 25 questions to study 8 of these will be on the exam I only have to write about 2
How many exam questions can I " eliminate " from studying
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1$\begingroup$ It's not clear what you mean here. In what scenario could you "eliminate" even one question from studying? $\endgroup$– Ben GrossmannDec 11, 2016 at 22:51
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2$\begingroup$ not all 25 of the questions will be on the exam . Only 8/25 will . And of those I get to PICK 2 . So if I prepare the questions in advance . I won't need to study some of them . $\endgroup$– Jordana CDec 11, 2016 at 22:54
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$\begingroup$ Yes! Exactly !!! That's the answer I need $\endgroup$– Jordana CDec 11, 2016 at 22:58
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$\begingroup$ @Peter I think the fact that you get to choose 2 of the 8 is significant $\endgroup$– Ben GrossmannDec 11, 2016 at 22:58
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1$\begingroup$ Knowing 19 out of the 25 guarantees getting 2 right, if 8 questions are presented and the rest may be ignored $\endgroup$– Ben GrossmannDec 11, 2016 at 23:00
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2 Answers
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The "worst case scenario" is when you study for 17 questions, and you got the remaining 8. So if you study 19 questions, then according to the pigeonhole principle, there will be surely 2 questions of the 8 that you will know. If you only want to know 1 question, then you need to learn 18 of them in the worst case.
(Trying to find worst case scenarios is usually not so helpful, because they are hard to define, so I generally don't recommend.)
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If you know $k \leq 19$ out of the $25$ questions, then the probability of getting at least two questions you know is given by $$ 1 - \frac{18\cdot\binom{25-k}{7}}{\binom {25}{8}} $$ If you know $11$, there is approximately a $94\%$ chance of success. Around $90\%$ if you know $10$. See WA.
answered Dec 11, 2016 at 23:10