# Probability Question - End Our Debate **URL:** \ **Category:** Factual Questions\ **Created:** [April 11, 2001, 4:00am UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557 "2001-04-11T04:00:45Z")\ **Posts on this page:** 13\ **Page:** 1
**Author:** ![Cyberhwk](https://avatars.discourse-cdn.com/v4/letter/c/7993a0/32.png) [@Cyberhwk](https://boards.straightdope.com/u/Cyberhwk)\ **Post date:** [April 11, 2001, 4:00am UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/1 "2001-04-11T04:00:45Z")
Situation: I’m in the car listening to a 15 track CD. I set the random play and pop in the CD. It proceeds to randomly play track 13. Then the random play makes it play 13 again. I am somewhat taken aback by this, pondering the odds of this happening. I try to take it up with my family but, like usual, a war breaks out. My sister believes that the odds of it playing the same song twice is 1 in 225. 1 in 15 for the first time, and 1 in 15 for the second. I agree under the condition that you had to have previously chosen a desired track (i.e., guess track 3 then random play somehow chooses 3 twice in a row.) But this is not what I am talking about. I say it is 1 in 15. There is a 1 in 1 chance that it will choose ANY track. Then a 1 in 15 chance that you will choose it again. Answers, questions, comments, inquires or complaints? ---
**Author:** ![riley\_dieffenbach](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@riley\_dieffenbach](https://boards.straightdope.com/u/riley_dieffenbach)\ **Post date:** [April 11, 2001, 4:11am UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/2 "2001-04-11T04:11:32Z")
Cyberhwk- You are correct. Congratulations you’ve won a new toaster oven. Much like the odds of rolling doubles on a pair of dice, a situation in which your odds are one in six. ---
**Author:** ![sethdallob](https://avatars.discourse-cdn.com/v4/letter/s/e36b37/32.png) [@sethdallob](https://boards.straightdope.com/u/sethdallob)\ **Post date:** [April 11, 2001, 4:34am UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/3 "2001-04-11T04:34:09Z")
I just love the OP’s sig. That’s all. Good night. ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [April 11, 2001, 4:41am UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/4 "2001-04-11T04:41:45Z")
Well, this depends a bit on semantics. The probability of picking track 13 at any given time is 1 in 15. The fact that track 13 was picked the first time does not affect the probability of track 13 being picked the second time. **BUT!**. The _total_ probability of both events taken as one: track 13 twice in a row, is indeed 1 in 225. There are 225 possible permutations of _two_ track selections. ---
**Author:** ![drachillix](https://avatars.discourse-cdn.com/v4/letter/d/48db29/32.png) [@drachillix](https://boards.straightdope.com/u/drachillix)\ **Post date:** [April 11, 2001, 4:50am UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/5 "2001-04-11T04:50:00Z")
> [@](#): > > \*Originally posted by friedo \* > god hates fundies I wandered through that link, I think I found a sig Amid thoughts of baseball Onan decides he doesn’t want to have a kid so he pulls out. Apparently God doesn’t like cumshots so God did away with Onan as well. (Genesis 38:7-10) For some reason this struck me as sooo funny, I’m still chuckling right now. ---
**Author:** ![kabbes](https://avatars.discourse-cdn.com/v4/letter/k/e99b99/32.png) [@kabbes](https://boards.straightdope.com/u/kabbes)\ **Post date:** [April 11, 2001, 2:04pm UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/6 "2001-04-11T14:04:22Z")
In case it isn’t clear from what has been said already: The chances of it playing the same track twice in a row (having just switched the thing on): 1 in 15 The chances of it specifically playing track 13 twice in a row (having just switched it on): 1 in 225 Please note though that if you leave the player going then the chance of it eventually playing the same track twice in a row goes to 1. As an aside: I was under the impression that random players they pick at random from the tracks that haven’t been played yet in the random cycle, until every track has been played once. The process then gets repeated. This would mean that you would have to have already been playing track 13 when you pressed the “random” button. The chance of it then picking 13 as the first on its random list would then, of course, be 1 in 15. ---
**Author:** ![Anachronism](https://avatars.discourse-cdn.com/v4/letter/a/e56c9b/32.png) [@Anachronism](https://boards.straightdope.com/u/Anachronism)\ **Post date:** [April 11, 2001, 2:36pm UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/7 "2001-04-11T14:36:09Z")
> [@](#): > > \*Originally posted by kabbes \* > \*\*As an aside: I was under the impression that random players they pick at random from the tracks that haven’t been played yet in the random cycle, until every track has been played once. The process then gets repeated. > \*\* Some CD players have ‘no repeat random’ play as an option, some automaticaly do it. Some of the cheaper CD players don’t have ‘no repeat random’ at all. ---
**Author:** ![Coldfire](https://avatars.discourse-cdn.com/v4/letter/c/a587f6/32.png) [@Coldfire](https://boards.straightdope.com/u/Coldfire)\ **Post date:** [April 11, 2001, 3:06pm UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/8 "2001-04-11T15:06:42Z")
> [@](#): > > \*Originally posted by kabbes \* > \*\*The chances of it playing the same track twice in a row (having just switched the thing on): 1 in 15 > > The chances of it specifically playing track 13 twice in a row (having just switched it on): 1 in 225\*\* I think I know what you mean, but you could have worded it even _more_ carefully. The way you state it, the first example has a 1 in 225 chance as well. A better way of saying it would be: _The chances of the CD player repeating the previous track whilst on random: 1 in 15_. See the difference? ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [April 11, 2001, 3:38pm UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/9 "2001-04-11T15:38:38Z")
> [@](#): > > \*Originally posted by Coldfire \* > \*\*See the difference? \*\* I don’t. It seems to be 1 in 15, like kabbes said. Riley’s example of a pair of dice seems appropriate. ---
**Author:** ![Cyberhwk](https://avatars.discourse-cdn.com/v4/letter/c/7993a0/32.png) [@Cyberhwk](https://boards.straightdope.com/u/Cyberhwk)\ **Post date:** [April 11, 2001, 5:35pm UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/10 "2001-04-11T17:35:55Z")
> [@](#): > > \*Originally posted by Anachronism \* > \*\* > Some CD players have ‘no repeat random’ play as an option, some automaticaly do it. Some of the cheaper CD players don’t have ‘no repeat random’ at all. > \*\* Gee . . .thanks. ---
**Author:** ![kabbes](https://avatars.discourse-cdn.com/v4/letter/k/e99b99/32.png) [@kabbes](https://boards.straightdope.com/u/kabbes)\ **Post date:** [April 12, 2001, 9:04am UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/11 "2001-04-12T09:04:16Z")
> [@](#): > > \*Originally posted by kabbes \*\*\* > > The chances of it playing the same track twice in a row (having just switched the thing on): 1 in 15\*\* > [@](#): > > \*Originally posted by Coldfire \*\*\* > > I think I know what you mean, but you could have worded it even _more_ carefully. The way you state it, the first example has a 1 in 225 chance as well. \*\* Not sure I see your problem **Coldie**. It’s like the old “What is the probability of 2 or more people in a room of 22 sharing the same birthday?” question. The “chance of it playing the same track twice in a row” (as I said) is Prob(playing any track) x Prob(playing that track again) = 1 x 1/15 = 1/15 so I don’t see what your beef with the way I worded my statement is. ---
**Author:** ![Coldfire](https://avatars.discourse-cdn.com/v4/letter/c/a587f6/32.png) [@Coldfire](https://boards.straightdope.com/u/Coldfire)\ **Post date:** [April 12, 2001, 9:39am UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/12 "2001-04-12T09:39:23Z")
Yeah, it was mostly semantics anyway - forget about it, you got the gist of it right from the get-go. ---
**Author:** ![galt](https://avatars.discourse-cdn.com/v4/letter/g/35a633/32.png) [@galt](https://boards.straightdope.com/u/galt)\ **Post date:** [April 12, 2001, 11:11am UTC](https://boards.straightdope.com/t/probability-question-end-our-debate/61557/13 "2001-04-12T11:11:16Z")
Also, talking specifically about the randomness in consumer electronics devices, it’s difficult to be precise about the probability of this-or-that event occurring, since you don’t know the algorithms they use. For example, just last week I wrote some software (for a consumer electronics device, no less) which picks a “random” number repeatedly, but it explicitly **excludes** the one which was last picked, so the probability of the same number being picked twice in a row is zero. For the C nerds, x = (x + RandomInRange(1,numTracks-1))%numTracks; 😃 But speaking of an ideal CD player which is truly picking randomly from all tracks on the disc, you’re right, Cyberhwk.