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?
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.
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.
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.
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.
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.
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.
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.
