Two Plus Two Older Archives  

Go Back   Two Plus Two Older Archives > General Gambling > Probability

Reply
 
Thread Tools Display Modes
  #1  
Old 07-25-2005, 07:38 PM
BruceZ BruceZ is offline
Senior Member
 
Join Date: Sep 2002
Posts: 1,636
Default Another theatre line problem

10 people stand in a single file line in front of a ticket window. The 10 people have 10 different heights. The ticket clerk can see a person if and only if no one taller stands in front of that person. How many people can the ticket clerk see on average?
Reply With Quote
  #2  
Old 07-25-2005, 08:00 PM
SheetWise SheetWise is offline
Senior Member
 
Join Date: Jul 2005
Location: Phoenix
Posts: 841
Default Re: Another theatre line problem

<font color="white">4 (I get 4.5)</font>
Reply With Quote
  #3  
Old 07-25-2005, 08:40 PM
zerosum zerosum is offline
Member
 
Join Date: Sep 2004
Posts: 40
Default Re: Another theatre line problem

[ QUOTE ]
10 people stand in a single file line in front of a ticket window. The 10 people have 10 different heights. The ticket clerk can see a person if and only if no one taller stands in front of that person. How many people can the ticket clerk see on average?

[/ QUOTE ]

Do patrons wearing hats count? [img]/images/graemlins/grin.gif[/img]
Reply With Quote
  #4  
Old 07-25-2005, 08:45 PM
BruceZ BruceZ is offline
Senior Member
 
Join Date: Sep 2002
Posts: 1,636
Default Re: Another theatre line problem

[ QUOTE ]
The ticket clerk can see a person if and only if no one taller stands in front of that person.

[/ QUOTE ]
Reply With Quote
  #5  
Old 07-25-2005, 08:49 PM
irchans irchans is offline
Senior Member
 
Join Date: Sep 2002
Posts: 157
Default Re: Another theatre line problem

Cute. My answer is below in white

<font color="white"> 2.93 on average </font>
Reply With Quote
  #6  
Old 07-25-2005, 08:55 PM
kyro kyro is offline
Senior Member
 
Join Date: May 2004
Location: Rochester, NH
Posts: 400
Default Re: Another theatre line problem

<font color="white"> I haven't done the math yet, but my instinct tells me it is lower than this</font>
Reply With Quote
  #7  
Old 07-25-2005, 08:58 PM
bobman0330 bobman0330 is offline
Member
 
Join Date: Aug 2004
Posts: 52
Default Re: Another theatre line problem

<font color="white"> The answer seems like it should be the 10th partial sum of the harmonic series.
The ticket taker can always see the first in line. There's a probability of .5 that the second person will be taller than the first. There's a probability of 1/3 that the third person will be taller than either of the first two, etc., etc.
1+1/2 + 1/3 + 1/4 + ... +1/10 = 2.929 </font>
Reply With Quote
  #8  
Old 07-25-2005, 09:47 PM
PairTheBoard PairTheBoard is offline
Member
 
Join Date: Dec 2003
Posts: 46
Default Re: Another theatre line problem

[ QUOTE ]
10 people stand in a single file line in front of a ticket window. The 10 people have 10 different heights. The ticket clerk can see a person if and only if no one taller stands in front of that person. How many people can the ticket clerk see on average?

[/ QUOTE ]

Begin Aborted Attempt
<font color="white">
There are 10! ways they can line up.

First arrange them in order 1,2...,9,10 to see all 10. One way to do this.

Number of ways to see exactly 9:
Choose any of the first 9 and move him back one or more places. So, 9+8+7+6+5+4+3+2+1 = 9(9+1)/2 = 45

Number of ways to see exactly 8:
Choose any two of the first 9 and move them back one or more places.

Yikes. There's got to be an easier way.
</font>
End Aborted Attempt

PairTheBoard
Reply With Quote
  #9  
Old 07-25-2005, 09:54 PM
KenProspero KenProspero is offline
Senior Member
 
Join Date: Jul 2004
Posts: 123
Default Re: Another theatre line problem

LOL, I started down the same way, and came to the same conclusion
Reply With Quote
  #10  
Old 07-26-2005, 12:11 AM
PairTheBoard PairTheBoard is offline
Member
 
Join Date: Dec 2003
Posts: 46
Default Re: Another theatre line problem

I think I've got it.

PairTheBoard
Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


All times are GMT -4. The time now is 03:51 PM.


Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2024, vBulletin Solutions Inc.