odds of exam questions scenario

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declan

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I have a scenario where I have a list of 30 subjects that might appear in an exam.

of the 30, only ten will actually appear in the exam and of those 10, I must select 5 to write a paragraph on.

Given that I have the list of thirty, how many paragraphs would I need to write to ensure that I would have at least 5 of the selected 10?

I am having trouble caluculating beyond the first event (each topic having a 1 in 3 chance of being part of the ten).

My instinct says 20, but I think it's likely less than that.

To clarify, my teacher says the learning outcomes are what is important, so having multiple paragraphs pre-prepared is not cheating.
 
If you were to prepare 20, your teacher could well set the exam on the other 10.

To ensure that you have 5 of the chosen 10, you would have to prepare 25 of the original 30 so that there are only 5 you have not prepared.
 
HallsofIvy said:
If you were to prepare 20, your teacher could well set the exam on the other 10.

To ensure that you have 5 of the chosen 10, you would have to prepare 25 of the original 30 so that there are only 5 you have not prepared.
Click to expand...

In that case, preparing 25 x 300 words (300 word paragraph is the required answer) leaves me writing 7500 words.

There must be an interesting 'tipping point' for say, a 90% or 85% chance of success that significantly reduces the required writing from 7500 words. Can you calculate that? I like to take a risk :)
 
declan said:
In that case, preparing 25 x 300 words (300 word paragraph is the required answer) leaves me writing 7500 words.

There must be an interesting 'tipping point' for say, a 90% or 85% chance of success that significantly reduces the required writing from 7500 words. Can you calculate that?
Click to expand...
How is "interesting" defined? What have you tried so far? What statistical methods have you applied? Where are you getting stuck?

Please be complete. Thank you! ;)
 
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