Cheap 'n' Nasty MP3 Player
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
My MP3 player is cheap 'n' nasty and has now broken: it is stuck on 'Shuffle'. In this mode it starts with whatever track you put it on, but then plays tracks in a random order. The only restriction is it never plays a song that's already been played that day.
I purchased my favourite murder mystery book in audio format, and put the first 6 chapters on my MP3 player. (Each chapter is exactly 1 track.) There's nothing else on my player at the moment. What is the probability that I will hear the 6 chapters in order as I listen today, without having to change tracks at all? (Obviously, I will ensure it plays chapter 1 first.)
The next day I empty the player before putting on the next 6 chapters. This time I also transfer a CD of mine with 11 songs on. I don't mind songs coming in between the chapters of my book, as long as the chapters are in order. What's the probability of that happening now?
Answer
With only 6 tracks on the player:
The first chapter has been set to play first. The probability of the next 5 chapters playing in order is 1/5! = 1/120.
With the music on the player as well:
Seeing as I don't care about when the music plays, it doesn't change anything. The answer is still 1/120.
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Comments
sweetpeao4o3  
Feb 02, 2005
| umm |
sweetpeao4o3
Feb 02, 2005
| that was weird |
Atropus  
Feb 02, 2005
| Wow - I failed statistics at high school but I got this one easily.. Thanks for the cool teaser ^_^  |
mizgolf13
Feb 03, 2005
| all righty then....  |
Jon0513 
Feb 05, 2005
| where did u get 1/5= 1/120? |
pi202
Feb 05, 2005
| john: 5! (five factorial) means 5x4x3x2x1 which equals 120. That's how 1/5!=1/120. |
(user deleted)
Feb 09, 2005
|  Math Wizard.... Way to go!! |
MrBasKetBall
Feb 13, 2005
| Too easy. |
munchtipq
Mar 18, 2005
| Argggh! I ALWAYS get taken in by these and go through all the math of calculating the probability only to get the same answer! I like it when that happens, though.  Good one |
lilwes2005
Apr 16, 2005
| that was a nice easy teaser thx i got the right answer |
brianz
Apr 30, 2005
| I got the first half but can't believe I missed the second half. |
BrownEyes
May 03, 2005
| Woah! |
bigSWAFF_69_
May 20, 2005
| my shuffle on my CD player is a lot more un-complex (is that a word?) You can program how ever many tracks you want to skip. Any way, good job. |
Yoyobug02
Jun 04, 2005
| Kinda hard i had to think about it but i finally got it good job! |
Beo921
Jun 14, 2005
| Good job. I like that you added the second part. I had to think about it more...  |
slat490
Jun 20, 2005
| Do u have an iPod suffle, cause i do and it dose the same thing only the battery dies ultra fast too. |
naughtyangel
Jul 01, 2005
| fun |
emcruiserchik
Jul 06, 2005
| I kept looking for some trick in it and ended up with a headache  briiliant! |
Desert660
Jul 28, 2005
| Dude ow do you do that????AneWayz cool   |
kickthecan
Dec 16, 2005
| Cool |
sugarnspice4u7
Dec 23, 2005
| you spelled favorite wrong.
oh well- good teaser! |
blackmarket69
Feb 22, 2006
| um.......ok? |
pi202
Feb 23, 2006
| Sugarnspice: I'm English. I spelt favourite perfectly thank you very much. |
Jimbo
Feb 27, 2006
| Firstly I'm not English but I can spell "favourite" so I guess that makes you the odd man out sugar (sic). Secondly, I loved the second part - nice twist!. Thirdly there was just one bit that wasn't clear in the wording. If you listen to the chapters shuffling all day then on one of the many random passes the 5 chapters might be in order. The answer implies that the 5 chapters are played just once. Threw me a bit! |
pi202
Feb 27, 2006
| Fair enough jimbo - I hadn't thought of your third point. The wording is a little ambiguous I admit. |
Jimbo
Mar 01, 2006
| My apologies Pi. It does say that it never plays a song that has already been played that day so that's my mistake. Good puzzle! |
buenos
May 09, 2006
| whoops... didn't read that you select the first one so I got 1/720 for both |
FatHead
Apr 06, 2007
| I hear you Munch. But all the more reason to give it a full Star! |
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