My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
January 28th, 2015, 12:54 AM   #1
Newbie
 
Joined: Jan 2015
From: Spain

Posts: 1
Thanks: 0

probablity - n previolusly persons failed exam (tricky)

We have an exam. Students are staying in queue. After every student probablity that professor finish exam is $\frac12$. For first student in queue there is $\frac12$ probablity that he pass. When first student fails exam then second student with probabality $\frac{1}{2+2}$ fail exam. And generally $k-th$ student fails exam with probablity $\frac{1}{j+2}$ where $j$ is number of students that failed exam. So potentially the best idea is to be last in the queue, but in this case we have the biggest probablity that proffessor finish exam before we try pass.

Find positions in queue that our probablity to pass is $\ge 1/2$

So look at my attempt:
We get $k$-th postiotn. Probablity that professor don't finish is $\frac{1}{2^{k-1}}$
And now let $N_0$ - 0 students failed exam
$N_1$ - one student failed exam
$...$
$N_{k-1}$ - $(k-1)$ students failed exam
$A$ - $k$-th student didn't failed exam.
So $$P(A)=\frac{1}{2^{k-1}}\sum_{i=0}^{k-1}P(A|N_i)P(N_i) = \frac{1}{2^{k-1}}\sum_{i=0}^{k-1}\frac{1}{2i+2}P(N_i)=\frac{1}{2^{k}}\sum_{i=1}^{ k}\frac{1}{i}P(N_{i-1}) $$
Now my problem is to compute $P(N_{i}). Could you help me, please ?
xaweyNEW is offline  
 
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
exam, failed, persons, previolusly, probablity, problem, tricky



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
(Failed) Proof: There are no odd Giuga numbers Hedge Number Theory 14 January 14th, 2013 12:30 PM
how to be member of any university's library,for persons ... johnmath Math Books 3 August 9th, 2012 12:44 PM
PRobablity daivinhtran Algebra 4 June 11th, 2011 07:52 PM
PRobablity daivinhtran Algebra 1 June 11th, 2011 07:07 PM
Differential equations! Need help with this.. tricky tricky johnnyboy23 Differential Equations 2 September 17th, 2010 10:20 PM





Copyright © 2019 My Math Forum. All rights reserved.