My Math Forum interesting probability question
 User Name Remember Me? Password

 Algebra Pre-Algebra and Basic Algebra Math Forum

 December 10th, 2008, 01:20 PM #1 Newbie   Joined: Dec 2008 Posts: 8 Thanks: 0 interesting probability question I was wondering what the formula would be to figure out this problem i thought of. If you have a CD with 19 songs on it and you play it on shuffle what would the probability be of it playing the CD in the correct order. Ignore the fact that the shuffle feature is faulty on MP3 players. It is just an example.
 December 10th, 2008, 01:29 PM #2 Newbie   Joined: Dec 2008 Posts: 8 Thanks: 0 Re: interesting probability question Would it be a permutation? 19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1= 121645100408832000
 December 10th, 2008, 02:13 PM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Re: interesting probability question 1/19! ??
December 10th, 2008, 02:54 PM   #4
Senior Member

Joined: Jul 2008

Posts: 895
Thanks: 0

Re: interesting probability question

Quote:
 Originally Posted by greg1313 1/19! ??
Does the "shuffle" function of MP3 players allow repetition?

December 10th, 2008, 03:12 PM   #5
Global Moderator

Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,968
Thanks: 1152

Math Focus: Elementary mathematics and beyond
Re: interesting probability question

Quote:
 Originally Posted by Dave Does the "shuffle" function of MP3 players allow repetition?
I don't think so, but I guess it depends on the manufacturer. The one I had would not play the same track twice, and would stop playing once it had gone through all of the songs.

In regards to the question:
My reasoning is as follows. At the start of playback there are 19 possibilities and only one is the first track, so the probability of it being played is 1/19. For the next song there are 18 possibilities and only one is the second track so the probability of it being played is 1/18. From my rather limited understanding of probability, this means that the odds of the first track being played first followed by the second track are 1/(18 * 19) or 1/342. Extending this pattern gives (I think) 1/19! or 8.22063525 X 10^-18. It is rather a slim chance, according to these numbers, but then, I could be wrong, of course.

 December 10th, 2008, 03:14 PM #6 Newbie   Joined: Dec 2008 Posts: 8 Thanks: 0 Re: interesting probability question for the sake of the question lets assume that there are no repeats.
 December 10th, 2008, 03:33 PM #7 Newbie   Joined: Dec 2008 Posts: 8 Thanks: 0 Re: interesting probability question would that be for the whole cd of 19 songs? The 1/19 would only apply for the 1st song being played in the correct order. for all 19 songs it would be: 1/(19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)= 1.21645100408832e+17 (I think)
December 10th, 2008, 03:46 PM   #8
Global Moderator

Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,968
Thanks: 1152

Math Focus: Elementary mathematics and beyond
Re: interesting probability question

Quote:
 Originally Posted by Kevlar93 would that be for the whole cd of 19 songs? The 1/19 would only apply for the 1st song being played in the correct order. for all 19 songs it would be: 1/(19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)= 1.21645100408832e+17 (I think)
Yes. Please forgive me I should have been more clear about what I meant. The ! after the 1/19! I typed means 19 factorial, that is 1*2*3...*19. I agree with your answer(the 1/(19*18*17...*1 part), but my calculator gave me 8.22063525 X 10^-18.

 December 10th, 2008, 03:58 PM #9 Newbie   Joined: Dec 2008 Posts: 8 Thanks: 0 Re: interesting probability question I did not know that the !=factorial you learn something new every day
 December 10th, 2008, 04:10 PM #10 Newbie   Joined: Dec 2008 Posts: 8 Thanks: 0 Re: interesting probability question 1/(19!)=8.22063524662433e-18 thank you

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Saunak Algebra 2 September 6th, 2013 10:22 AM alpha_century Probability and Statistics 0 May 5th, 2013 11:22 AM superconduct Probability and Statistics 6 March 9th, 2012 06:38 AM hoyy1kolko Probability and Statistics 3 July 16th, 2011 12:35 AM hoyy1kolko Probability and Statistics 4 July 9th, 2011 12:36 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top