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Simple Statistics Problem

by heavysm
2 replies
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I can't easily find this online, nor is it an actual problem, but I am pretty sure there is a definable answer I just can't figure out (currently reading/ studying for finals so i can't give this more thought).

Out 8 possible essay prompts 5 will be listed on the final and we must write on 3 of our choice of those 5. How many out of those 8 overall prompts can i pick out and still be safe knowing i prepared for x number (5, 6 - 7...whatever number it is) with there being a statistically high chance that those questions i picked will be on the exam, no matter which i pick.

This is more for personal knowledge than actual application. I just don't know the answer nor how I would get it.
  • Profile picture of the author williambrown
    My mind is not working today, I didn't understand anything maybe I will try to look at it again
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  • Profile picture of the author Alexa Smith
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    Originally Posted by heavysm View Post

    Out 8 possible essay prompts 5 will be listed on the final and we must write on 3 of our choice of those 5. How many out of those 8 overall prompts can i pick out and still be safe knowing i prepared for x number (5, 6 - 7...whatever number it is) with there being a statistically high chance that those questions i picked will be on the exam, no matter which i pick.
    You're making it harder than it is, I think: it has nothing to do with statistics, really. It's just an arithmetical question.

    You'd need to learn any six of the eight possible questions, to guarantee being able to answer three in the exam.

    If they're selecting five from a possible eight questions, then the worst that can happen, if you learn six, is that three of the six you learn will happen to be the exact three not selected by the examiners, and even in that unlucky case the other three (and probably more, in reality) must be there. It's no more difficult than that, I think? How easy it is to learn six questions is, of course, another matter.

    (If you learned only five, instead of six, then the probability of not having three out of your five selected for the exam is very small. You need factorial numbers to work this out, but most of the equation cancels out, leaving you 1/56, and you'd therefore still be ok for three questions about 98% of the time. Learn any five questions, and you have only about a 2% risk of an accident, in other words.)

    Good luck!
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