wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> hard >> Random Flying Cards
        
(Message started by: fatball on Jan 22nd, 2006, 8:53pm)
Title: Random Flying Cards
Post by fatball on Jan 22nd, 2006, 8:53pm
A standard pack of cards is thrown into the air in such a way that each card, independently, is equally likely to land face up or face down.  The total value of the cards which landed face up is then calculated.  (Card values are assigned as follows: Ace=1, ..., King=13.  There are no jokers.)

What is the probability that the total value is divisible by 13?
Title: Re: Random Flying Cards
Post by Barukh on Jan 23rd, 2006, 11:07am
Card throwing probability (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_putnam;action=display;num=1135896221) is a similar problem discussed recently.
Title: Re: Random Flying Cards
Post by fatball on Jan 23rd, 2006, 11:21am
Yes, you are right.  Both [hide]partition probability[/hide] and [hide]generating functions[/hide]  can be used to deal with the problem.
Title: Re: Random Flying Cards
Post by Eigenray on Jan 24th, 2006, 5:40am
Generalizing to k decks of n cards each, I get
2-kn 1/n [sum]d|n, d odd phi(d) 2kn/d.


Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board