Law student looking for math help

This shouldn't be too hard...
So I have an exam tomorrow, I would like to study as little as possible for it, and I would like you to tell me what are my chances of succeeding:

There are 9 topics in the module.
There are 6 questions in the exam.
The exam is divided into two sections (3 questions in each section).
One must answer 1 question per section.

If one studies 5 topics out of the 9, what are the chances that he won't be able to answer any questions in one section. (i.e. what are the chances of failure).

If I understand properly you must answer one of three questions in section 1 and also one of three in section 2. You want to know what the propbability is of none of the three questions in section 1 or none of the three in section two being among the 5 topics you studied, right?

If we assume that the topics are randomly selected, the chance that none of the three questions in section 1 are among the 5 you studied is (4/9)^3 = 8.8%. Since you must suceed on both sections 1 and 2, the chance of suceeding on both is (1-0.088)^2 = 83% if the topics are randomly selected. Hence the chanec of failing the exam is 1 - 0.83 = 17%

However, I suspect that the topics aren't random - I wouldn't expect that two or even all three questions could be on the samed topic, right? If this is true then the chance of all three questions on section 1 not being among the five is (4/9 x 3/ 8 x 2/7 ) = 4.7%. If it's required that all 6 questions be on 6 different topics then you are gurarranteed to get one section correct (because out of 6 questions at least 2 must be from topics you've covered). So you will fail if you fail section 1 or if you fail section 2. That probability is twice what we determined earlier, or 9.4%.

As you can see it makes a big difference whether topics may be repeated or not.

You have certainly understood properly. That is exactly what I was looking for. Thank you very much.

It's not possible that all three questions are on the same topic, but it is possible that 2 out of the 6 questions are.

In both cases, I think it's worth the gamble. Right?

Quote:

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Originally Posted by wanitto

In both cases, I think it's worth the gamble. Right?

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Obviously that's your call, not mine. If you could be proficient in 6 topics rather than 5 your odds improve significantly, and at 7 topics you're at 100% success. I think you should also think about the possibility that you may have difficulty even if the question is from one of the topics you studied, so having two questions in each section that are from topics you're comfortable with could really help your chances.

remind me never to hire you as a lawyer, but good luck