An instructor gives her class a set of $10$ problems with the information that the final exam will consist of a random selection of $5$ of them. If a student has figured out how to do $7$ of the problems, what is the probability that he
or she will answer correctly
(a) All $5$ problems?
(b) At least $4$ of the problems?
How do I find this probability because the fact that she knows 7 of the qustions is what is throwing me off? I know you have to find $\frac{\#E}{\#S}$ and $\#S= \binom{10}5$, but I am confused with the rest of the problem.
Best Answer
It seems to me, specifying the problem would help.
So there are 10 questions in total. Let's number them like this: Questions a-1~ a~10.
Now, the student knows how to solve 7 of them. Let those be a-1 ~ a-7.
It really doesn't matter which of these 10 specific questions the student knows, just the fact that she knows one specific set of 7 questions is important. That being said, no need to use 10combination7.
Now, the first one asks for the probability of the random 5 questions the teacher chooses being included in the a-1~ a-7.
7C5/10C5.
The second question,
would be the probability of choosing 4 + choosing 5, thereby being (7C4 x 3C1 + 7C5)/10C5
Thank you ozipone for pointing out my mistake:)
Hope this helps.