Probability brain teaser for you guys.

parc

I'm trying to figure out this simple question out but not really sure how you do it.

Ok, say there is an exam coming up.

There are 10 lectures in the module.
In the exam you need to answer 2 question out of 5 options
How many lectures should I study to have a good chance of covering the material to do well in the exam?

(Note assuming that each question will be based on only one of each lecture and that I'm trying to be economical with my study. (i.e. the safest thing to do is to study 10/10 but this isn't economical. Studying just 2 topics would be too much of a gamble - I think it gives you a 22% chance of covering the material if my calculations are correct...so maybe covering 3 topics really well and 2 as back up would be best? But how is this done using probability???)

parc

Actually is this the right way to do it?

Say I choose to study 4 topics, the probability of 2 of my 4 studied lectures coming up is approximately 48% because

1/10+1/9+1/8+1/7 = 0.47896825396

That would raise to 65% if I choose to study 5 lectures because

1/10+1/9+1/8+1/7+1/6= 0.6456

Is this right?

ray giraffe

Long answer:
http://en.wikipedia.org/wiki/Lottery_mathematics

Medium answer:

=HYPGEOMDIST(0,3,5,10) is the formula in Excel for the probability that you study 3 questions and 0 of them come up when 5 topics out of 10 come up on the exam paper.

=HYPGEOMDIST(1,3,5,10) is the probability that you study 3 questions and 1 of them comes up

=1-HYPGEOMDIST(0,3,5,10)-HYPGEOMDIST(1,3,5,10) is the probability that you study 3 questions and at least 2 come up that you studied

Short answer
The probabilities you are ok when you study 1,2,3,4,5,6,7 questions are 0%, 22%, 50%, 74%, 90%, 98%, 100% respectively.

tolosenc

Intuitively, you'd have to study 7 to be certain of getting 2 questions you can answer.