Dewey

Jul 16, 2005, 08:15 PM

I have an audio CD with ten tracks on it. If I was to insert the disc into my CD player and select the "random" play function, what is the probability of all the tracks playing in the right order?

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Dewey

Jul 16, 2005, 08:15 PM

I have an audio CD with ten tracks on it. If I was to insert the disc into my CD player and select the "random" play function, what is the probability of all the tracks playing in the right order?

Emrysgirl

Jul 16, 2005, 09:22 PM

That's easy

1 in 10^10

Take the first song played. The chance that it's the first on the list is 1/10. Same for the second song played and the second on the list etc. They're all independant, so just multiply the individual probabilities.

1 in 10^10

Take the first song played. The chance that it's the first on the list is 1/10. Same for the second song played and the second on the list etc. They're all independant, so just multiply the individual probabilities.

arach

Jul 17, 2005, 10:33 AM

Nice answer. I was never good in that probability stuff. ;)

Dabney

Jul 19, 2005, 10:50 AM

the propability that the first song is the right song is 1/10. The probability for the second song then is 1/9 and so on. For the overall probability you have to multiply everything:

1/10 x 1/9 x 1/8 x 1/7 x 1/6 x 1/5 x 1/4 x 1/3 x 1/2 x 1/1

= 1/(10!) = 1/3628800 = 0.00002756 %

But i'm not really sure...

1/10 x 1/9 x 1/8 x 1/7 x 1/6 x 1/5 x 1/4 x 1/3 x 1/2 x 1/1

= 1/(10!) = 1/3628800 = 0.00002756 %

But i'm not really sure...

admin

Jul 19, 2005, 10:59 AM

The probability for each track is the same. Remember that despite track 1 being played it is still a 1/10 chance it could infact be played again!, therefore

1/10 to the power of 10 is correct.

Which would be 1/1000000000 or something like that.

1/10 to the power of 10 is correct.

Which would be 1/1000000000 or something like that.

Emrysgirl

Jul 19, 2005, 11:05 AM

No, don't bother, I'm sure of my answer. Look at my explanation. As adimn said, the probability of each song playing when it should is independant b/c the songs can be repeated.

As to the number, you're almost right admin: you're off by one 0.

1/10000000000

As to the number, you're almost right admin: you're off by one 0.

1/10000000000

Dabney

Jul 19, 2005, 11:22 AM

I don't agree...

the task is, that the ten songs are played in the right order, so no song can be played twice. Otherwise one song would be missing.

So you have ten possibilities for track 1, and as only one song is right the probability is 1/10. Then there are only 9 songs left, so the probability for track 2 is 1/9. Then there are only 8 songs left, so the probability is 1/8 and so on. :Smart:

the task is, that the ten songs are played in the right order, so no song can be played twice. Otherwise one song would be missing.

So you have ten possibilities for track 1, and as only one song is right the probability is 1/10. Then there are only 9 songs left, so the probability for track 2 is 1/9. Then there are only 8 songs left, so the probability is 1/8 and so on. :Smart:

Emrysgirl

Jul 19, 2005, 11:52 AM

I don't agree...

the task is, that the ten songs are played in the right order, so no song can be played twice. Otherwise one song would be missing.

So you have ten possibilities for track 1, and as only one song is right the probability is 1/10. Then there are only 9 songs left, so the probability for track 2 is 1/9. Then there are only 8 songs left, so the probability is 1/8 and so on. :Smart:

When you calculate the total possibilities, you don't assume the desired outcome. You're calculating the probability GIVEN that a song CAN'T repeat before all the songs have been played. But, that's a component of the situation you're looking for, not a rule.

The numerator is the number of favorable outcomes. That we all agree is 1.

The denominator is the total number of possibilities, favorable and not. That includes things like 1232532. That is, one of the undesired possibilities, or one way it could mess up is by repeating the tracks.

the task is, that the ten songs are played in the right order, so no song can be played twice. Otherwise one song would be missing.

So you have ten possibilities for track 1, and as only one song is right the probability is 1/10. Then there are only 9 songs left, so the probability for track 2 is 1/9. Then there are only 8 songs left, so the probability is 1/8 and so on. :Smart:

When you calculate the total possibilities, you don't assume the desired outcome. You're calculating the probability GIVEN that a song CAN'T repeat before all the songs have been played. But, that's a component of the situation you're looking for, not a rule.

The numerator is the number of favorable outcomes. That we all agree is 1.

The denominator is the total number of possibilities, favorable and not. That includes things like 1232532. That is, one of the undesired possibilities, or one way it could mess up is by repeating the tracks.

Emrysgirl

Jul 19, 2005, 11:59 AM

Here's a simmilar situation. It might be easier to understand with hard objects.

You have three marbles: green, blue and clear.

You want to pick the marbles from an opaque bag in that order (G-B-C)

You pick the first marble, the chances of it being green are 1/3.

You put it back. This may be the confusing step. The song just played is still on the CD and can still be chosen randomly.

Just because you want the next one to be blue doesn't mean it can't be green.

The probability of picking blue is 1/3.

You put that marble back, the third probability is 1/3.

Multiply them together b/c the outcome of one pick doesn't affect the next.

Trust me, I'm absolutely sure of my answer. I love probability.

You have three marbles: green, blue and clear.

You want to pick the marbles from an opaque bag in that order (G-B-C)

You pick the first marble, the chances of it being green are 1/3.

You put it back. This may be the confusing step. The song just played is still on the CD and can still be chosen randomly.

Just because you want the next one to be blue doesn't mean it can't be green.

The probability of picking blue is 1/3.

You put that marble back, the third probability is 1/3.

Multiply them together b/c the outcome of one pick doesn't affect the next.

Trust me, I'm absolutely sure of my answer. I love probability.

arach

Jul 19, 2005, 12:26 PM

Dabney is right, because if you choose "shuffle" on a CD player, no song will be repeated till every song has played. Therefore, when 1 song has played, it won't be played again, so the probability for the next track is 1/9.

It's the same with winamp shuffle btw.

It's the same with winamp shuffle btw.

admin

Jul 19, 2005, 12:29 PM

I guess it depends on whether you are talking about independant or dependant probability

Dabney

Jul 19, 2005, 12:30 PM

thanks, arach:D .

I understand all of your thoughts, emrysgirl, and it's all correct if you understand the question like that. But i understand it differently.

I understand all of your thoughts, emrysgirl, and it's all correct if you understand the question like that. But i understand it differently.

Emrysgirl

Jul 19, 2005, 12:36 PM

Yes, I suppose it all depends on the CD player used. Mine repeats without finishing all the songs.

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