Edit: This is NOT a homework question! It is a real life math problem. I have this exact situation coming up. I have not taken many math courses and don't know how to solve it. Please help!


There are 70 possible questions for a upcoming exam known in advance. I must solve the questions before the exam and memorise the solutions.

Of these 70 questions the professor will pick 12, of these 12, I will need to answer 8.

If I skip solving 4 questions pre-exam, it won't matter because I am allowed to skip 4 on the exam.

But if I skip solving 5 questions on the exam, what is the likelihood that all 5 of these will be included in the 12?

If I skip 6 what is the likelihood that at least 5 of these will be in the 12?

If I skip 10 what is the likelihood that at least 5 of these will be in the 12?

How many questions can I skip before it becomes relatively likely that I won't be able to answer 8 of 12?

Sorry, but AMHD has a posted policy of not doing homework.

Have you worked out a formula for this problem?

This is not a homework question. I am a philosophy student and I have an upcoming exam with this exact situation. I am not good at math, I don't know anything about probability.

I had moved this thread to Homework, but then moved it back to Mathematics. Judy had nothing to do with that, so I have reported that post to remove the unfair reddie you gave her.

One of our math experts may come along to untangle all the probability situations for you. I see you have posted this elsewhere also.

I moved this thread to Homework. Judy had nothing to do with that, so I have reported that post to remove the unfair reddie you gave her.

One of our math experts may come along to untangle all the probability situations for you. I see you have posted this elsewhere also.

What is a reddie, what is unfair? Am I not allowed to post elsewhere? I am new to this website. How do I get someone who knows about math to answer my question?

A reddie is a mark against my record of answering questions for giving you inaccurate or incorrect information.

We are all volunteers here. The way to get an answer is to wait for someone who can and is willing to answer your question to come along.

What is a reddie, what is unfair? Am I not allowed to post elsewhere? I am new to this website. How do I get someone who knows about math to answer my question?You gave Judy an "inaccurate," a reddie, but apparently were able to remove it. Yes, you can post anywhere on the 'Net. We are not a chat site, so please be patient. A math expert will eventually see this.

Why not study for all 70 questions and be totally safe?

I would study all of them. There is no possible way to know in advance which ones will be chosen by the professor. It would help to memorize the formulas, rather than the answers.

This has been posted before along very similar lines - but, as usual, I can't find it.

Thanks for your help ladies! I appreciate your efforts.

Unfortunately it is not a math test but a philosophy test so there are no formulas. Each question takes about an hour to work out, and it is a 2 hour exam, hence the problem.

Now I am really just curious of how to solve this math problem, but I think I will ask my boyfriend's friend she is an actuary.

Thanks again.

I'm not a mathematician.
'How many questions can I skip before it becomes relatively likely that I won't be able to answer 8 of 12?' What good does 'relatively' do you? You have to know 8. Even if you happen to skip 8 and those are in the 12 (regardless of the slim chance), you lose by knowing only 4. If you skip 7, you know only 5, 6, you know only 6, 5, you know only 7, 4, you now know the required 8. So you can only skip 4. Knowing odds is no help because I assume that you don't get partial credit for knowing less than 8.

If the goal is to be able to answer any 8 of the 12, then the odds work out as follows:

If you don't know the answer to 5 questions of the 70, the odds of being able to answer at least 8 of 12 randomly selected questions is 99.75%

If you don't know the answer to 6 of the 70, the odds of being able to answer at least 8 of 12 randomly selected questions is 99.3%

If you don't know the answer to 10 of the 70, the odds of being able to answer at least 8 of 12 randomly selected questions is 93.9%

If you don't know the answer to 20 of the 70, the odds of being able to answer at least 8 of 12 randomly selected questions is 53.3%, and for 21 it's 48.5%. So at 21 you are likely to not be able to answer at least 8 questions correctly.

It's interesting that in order to be able to answer 2/3 of randomly selected questions (i.e. at least 8 of 12), you must have studied slightly more than 2/3 of all the questions.