iPod/Probability/Odds

[flip_flop]

Not sure I'm in the right Topic, but here goes.

I have 12,482 songs on my iPod, 2 of which are by Franz Ferdinand.

Whenever I listen to my iPod I always use the shuffle feature and this morning, on my walk to work, the Franz Ferdinand songs came on one after the other.

What are the chances of that happening?

[fo3nix]

About a 6x10^-7 % chance.

However, this is pure probability. It assumes that the algorithm in your iPod selects songs purely randomly. Firstly, this is a rare thing to do (true randomness is pretty hard), and secondly, it's probably engineered to deliverer songs that overlap in some way, so that you enjoy the flow of music better.

[flip_flop]

Thanks for that - your second paragraph makes a lot of sense. Unfortunately, my maths finished at 'O' Level, so I have no idea what the first part means!

[jake-the-peg]

You have to be really carefull in probability about what question you are asking.

If you are asking what is the probability of switching on and these two coming up in a line that is one question.

If you are asking what is the probability of these two coming together at one point during your many walks to work that is another.

Do you have other Franz Ferdinand songs or is there just two - this affects the odds

Is the order important?

If you are asking what is the probability of any associated songs coming together that is yet another.

If two other songs by th same artist came together you would doubtlessly be asking the same question about that other band.

People are often surprised by "coincidences" but these are often less improbable than they think - we are almost all very bad at probabilities.

The classic is

"How many people do you need to selcet at random before there is a 50% chance that 2 will have the same birthday?"

The answer?

23

http://en.wikipedia.org/wiki/Birthday_problem

[4getmenot]

Non on mine I hate franz ferdinand

[Helveticus]

Hi there flip_flop, If your 2 Franz Ferdinand songs are A and B, then to get one Franz Ferdinand song immediately after another, your iPod would have to play either (A then B), or (B then A).
The probability of (A then B) is (1/12482) x (1/12482) = 6.4x10^-9
The probability of (B then A) is (1/12482) x (1/12482) = 6.4x10^-9
The overall probability is the sum of these i.e. 1.3x10^-8. This means that it should happen about once every 80 million times. Note if other groups have more than one song on your iPod, the chance that two songs by *any* group (i.e. not necessarily by Franz Ferdinand) are played in succession will be much higher. All this assumes, however, that the shuffle feature really selects songs randomly. As fo3nix correctly wrote, this is almost certainly not the case.

[fo3nix]

Just a note: I performed the same calculation that Helveticus did, but didn't take into account the fact that it could be song A then song B, or song B then song A. It doesn't really change the outcome though; adding two very small numbers still gives a very small number.

[factor-fiction]

The question here is after you have heard a Franz Fernidand track what are the odds that the next will be your other FF track. The chances are 1 in 12481.
But suppose you have 6241 groups on there, each with 2 tracks. The odds of any track being followed by another from the same group fall to 1 in 6240.

[factor-fiction]

Most people seem to have assumed you multiply the two probabilities. That is only valid if you played just two tracks from 12482 and wanted to know chance of getting a FF and a FF.
But of course when you pay an ipod you will always get a track . When the first FF track came on you wouldn't say "wow, FF, that's amazing, a 1 in 12482 chance.." What's important is the chance of the second one happening.

[mibn2cweus]

Once something happens all bets are off. Only a fool would wager against an already realised outcome. The odds that anyone of us exist are cosmological. Just the odds of having made it to the egg first is, by itself, pretty remarkable. I feel really lucky . . . but I'm not gambling on the remote possibility that I will ever happen again . . . not that once wasn't enough. ;o)