# The desired exam question paper (probability question)

• Aug 24th 2011, 10:55 PM
Narek
The desired exam question paper (probability question)
There is an exam. There are 25 exam question papers for 25 students who are lined up outside of the classroom. Each time, a students gets into the classroom, pick one paper (RANDOMLY) and go, sits on its desk and start his exam.

You are the 5th person in the line, who has to go to the class and pick a paper. Among those 25 papers, there is only 1 paper which questions are familiar to you.

Now the problem is: What is the probability that you will go into the classroom, and pick that one paper you want. (In other word, the probability that NO other student before you, will pick that exam paper which questions are familiar to you)

• Aug 25th 2011, 06:26 AM
Soroban
Re: The desired exam question paper (probability question)
Hello, Narek!

The problem seems to be very simple.
Perhaps I'm misinterpreting it?

Quote:

There is an exam. There are 25 different exam papers
for 25 students who are lined up outside of the classroom.
Each student enters the room, randomly picks a paper and starts his exam.

You are the 5th person in the line, who has to enter the room and pick a paper.
Among those 25 papers, there is only ine paper whose questions are familiar to you.

What is the probability that you will enter the classroom and pick that one paper?
That is, the probability that NO other student before you will pick that exam paper.

Let that special exam paper be called the "Exam".

For you to get the Exam, it must be the fifth one selected.
The probability that the Exam is the fifth one chosen is: .$\displaystyle \frac{1}{25}$

For you to get the Exam, the first four students must NOT get the Exam,
. . then you must get the Exam.

This probability is: .$\displaystyle \frac{24}{25}\cdot \frac{23}{24}\cdot\frac{22}{23}\cdot \frac{21}{22}\cdot \frac{1}{21} \;=\;\frac{1}{25}$

• Aug 25th 2011, 09:10 AM
MAX09
Re: The desired exam question paper (probability question)
that was an elegant way to solve the problem SOROBAN....
• Aug 25th 2011, 09:21 AM
CaptainBlack
Re: The desired exam question paper (probability question)
Quote:

Originally Posted by Narek
There is an exam. There are 25 exam question papers for 25 students who are lined up outside of the classroom. Each time, a students gets into the classroom, pick one paper (RANDOMLY) and go, sits on its desk and start his exam.

You are the 5th person in the line, who has to go to the class and pick a paper. Among those 25 papers, there is only 1 paper which questions are familiar to you.

Now the problem is: What is the probability that you will go into the classroom, and pick that one paper you want. (In other word, the probability that NO other student before you, will pick that exam paper which questions are familiar to you)