Help me determine chance of encountering a question

[wiseheart]

Okay, help me those of magnificent math skills.

I had to take an final consisting of 50 questions.
The professor said the final drew from a question
bank of 700 questions.

In order to study, we are advised to review 13 practice
exams. Each which have 10 questions. I took each quiz
an average of 10 times for a total of 130 quiz attempts.

Question Bank=700 Questions
Final=50 questions
Quiz=10 questions
#of quizzes=13
Attemptsateach=10

What is the probability of encountering all 700 questions
or what is my expected amount of questions to have encountered?

Ok go! Thanks!

[wiseheart]

Now that I have more time to specify, what I am looking for is what is the probability that I will have seen all 700 questions by taking the 13 quizzes of 10 questions each, and what is the probability of me having seen all 50 questions on the final beforehand via me taking the quizzes.

Basically, I am upset because the prof said if you take the quizzes enough time and know all the answers then you will be able to do fine on the final. When I encountered the final I would say 25-45% of the questions I had not ever seen before. So, I feel like either
A) Professor puts in new questions that are not in the question bank for the quizzes
or B) There are a lot more than 700 questions in the actual question bank.
or C) I'm wrong and statistic probability will show me the answer.

Thanks for any help.

[T50_Omaha8]

Let me get this straight.

You took 13 practice quizzes, each of which selected 10 questions randomly out of a 700 question bank?

You must relaize the maximum number of questions you are exposed to is 130, right?!? Since each question has a 1/70 chance of being on a quiz, the probability you have seen any random question P(Qi)
= 1 - P(not Qi)
= 1 - (69/70)^13
= 1 - .8294
= .1706
The expected number of questions you have seen of the 700 existing questions is 119.

Then the final is composed of 50 random questions from that 700 question bank?

The probability you've seen all of them is C(113,50)/C(700,50)--a number akin to (1/7)^50...you're far more likely to win the jackpot at keno than you are to have seen all these questions.

The fact that you had not seen ONLY around a third of the quesitons on the test makes me think the question bank was actually much smaller--more like 200 questions. If it really was 700 possible questions and you recognized 2/3 of them by going over a maximum of 130 questions before the test, you just got lucky enough to win the lottery.

I think you post in the O8 forum a lot as a pretty good player, so I don't take you for a total fool. Am I reading your question wrong?

Edit: I AM reading it wrong. There were 13 quizzes, you took them 10 times EACH. Now we have randomness problems. Did each of the 13 practice quizzes cover a specific subset of the 700 questions? I assume they must, since if they didn't it would just be one practice quiz. If there was one quiz with a huge subset and the other quizes had smaller ones, coming accross lots of unknown questions would be pretty probable.

But if each of them contains, say 60 questions (to leave a margin), then you should have seen at least 80% of the 700 questions (figured by computing probability of one certain question then multiplying by 700--so this undershoots how many questions you should actually have seen considerably...90% of the total is probably more like it). I think you did get gyped somehow.

[wiseheart]

T50,

Thanks a lot for answering my question. Sorry that it was a bit confusing the first time I worded it. Yes I took each quiz 10 times each.

I am going to ask the professor for more information. Once
I do, If you could figure out a mathematical formula that
shows the probability for me I will gladly ship you $10 on Stars.

Thanks.

[wiseheart]

Scratch my offer, my Professor got pissy when I probed
for more information. He did admit that he was wrong
and it was a pool of 1044 questions not 700. He also
made some points about how we can't draw much from
one instance. So, I don't think i am going to sway him
with any statistical analysis.

[T50_Omaha8]

Heh, sorry man.