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December 10th, 2008, 01:20 PM   #1
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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.
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December 10th, 2008, 01:29 PM   #2
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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
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December 10th, 2008, 02:13 PM   #3
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Re: interesting probability question

1/19! ??
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December 10th, 2008, 02:54 PM   #4
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Re: interesting probability question

Quote:
Originally Posted by greg1313
1/19! ??
Does the "shuffle" function of MP3 players allow repetition?
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December 10th, 2008, 03:12 PM   #5
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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.
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December 10th, 2008, 03:14 PM   #6
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Re: interesting probability question

for the sake of the question lets assume that there are no repeats.
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December 10th, 2008, 03:33 PM   #7
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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)
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December 10th, 2008, 03:46 PM   #8
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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.
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December 10th, 2008, 03:58 PM   #9
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Re: interesting probability question

I did not know that the !=factorial

you learn something new every day
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December 10th, 2008, 04:10 PM   #10
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Re: interesting probability question

1/(19!)=8.22063524662433e-18

thank you
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