Math Is Fun Forum

steven Atkinson

Guest

What are the chances of that!

Okay guys - I have come to this website to help me solve the following real life probability question that happened to me...

Basically I have an iPod with 3125 tracks.  I only have 1 B52's track on the iPod (Love Shack if you are interested!).  Now I listen to the iPod on shuffle mode - What happend to me was that the track that the iPod chose to play for track 52 was (you guessed it) B52's Loveshack!

My question is - what are the chances of that?

Thanks in advanced.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: What are the chances of that!

Unless I'm missing something that would make the question more complicated, it would just be 1 in 3125.

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Why did the vector cross the road?
It wanted to be normal.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: What are the chances of that!

Ahhh, I see.  Numerology is at work here.  52nd track is the B52.  The thing is, math doesn't care about similarities.  It would have been no more significant if the 52nd track was "52 Red Balloons".  Would you have found it significant if the 21st track was the B52's and you could only play it half way through before you had to stop listening?  Or if the 25th track was the B52's?  There are so many different things which we would find significant, it's hard to not see something.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

steven Atkinson

Guest

Re: What are the chances of that!

Okay, lets rephrase the questions... What are the chances of the 52st random track (out of 3125 tracks) being the only B52’s track on the iPod? 
Are you saying that this question does not have a mathematical answer?  Or can a value be placed on it?  For example the chances of the first random track being the B52’s song is 1/3125... is there not something similar that can be put on the chance of the 52nd random track being the B52’s track? Or am I missing the point????
Regards

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: What are the chances of that!

For example the chances of the first random track being the B52’s song is 1/3125... is there not something similar that can be put on the chance of the 52nd random track being the B52’s track?

Yes... it's exactly the same, 1/3125.  You see a similarity in numbers as being "special" and "less likely".  It isn't.  Because probability does not care about names.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: What are the chances of that!

This is simply out of interest for the computer science people.  If it is entirely random, it's 1/3125.  However, many players now use starvation queues in order to make it unlikely that a song plays twice over a short period of time.  The way it might work (there are many possible ways) is a random variable is first selected from 1 to 10.  If 1 to 5 is selected, a song from is randomly selected from the front of the queue.  If 6 through 8 is selected, the middle, and 9 or 10, the back.  When a song is played, it is moved to the back of the queue.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: What are the chances of that!

Wow!  I love the queue-biasing random song shuffle you described.  That's cool!

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igloo myrtilles fourmis

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: What are the chances of that!

Neat, I hadn't heard of a starvation queue.

I made a player once and just kept an array of recent songs so I would know what not to play. When developing I accidentally let the array grow to the size of the available songs and wondered why it froze.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

steven Atkinson

Guest

Re: What are the chances of that!

Okay, maybe I need to add some more info to the question... When the iPod is on random it plays the entire catalogue in a random sequence - it will not play the same song twice until it has played all the songs.  I would except that the chances of the 52nd track being the B52's song if during every selection it could choose from the entire catalogue... but thats not what i am saying... Am I making sence?  I can not believe for a second that the chances of the 52nd track to be the only B52's track is only 1/3125... (based on the random way the iPod plays the catalogue)  Somebody - help me out!!!!!!