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RED  box contains 64510 red  numbered balls: {R1,R2,...,R64510}  
BLUE box contains 65536 blue numbered balls: {B1,B2,...,B65536}  

1st person: takes a Red and a Blue, records the numbers like (Rx,By) 
            and puts them back inside.  
2nd person: does the same.  

1a) What is the possibility that both people will draw the same (Rx,By) ?
1b) If the whole process is repeated, what is the possibility of this happening again ?

RED box remains as is: 64510 red  numbered balls: {R1,R2,...,R64510}  
GREEN  box contains 256 green  numbered balls: {G1,G2,...,G256}  
YELLOW box contains 256 yellow numbered balls: {Y1,Y2,...,Y256} 

2a) What is the possibility that both people will draw the same (Rx,Gy,Yz) ?
2b) If the whole process is repeated, what is the possibility of this happening again ?

This is not a math homework, i am designing an application protocol, and i will use the method with the smallest collision possibility.
Thanks in advance :-)

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1 Answer 1

up vote 2 down vote accepted

(1) There are $64510\cdot65536$ possible pairs, to the probability of an exact duplication is $\frac1{64510\cdot65536}$. The probability of this happening twice in a row is the square of that number, $\left(\frac1{64510\cdot65536}\right)^2$.

(2) The principle is the same. There are $64510\cdot256\cdot256$ possible triples, so the probability that the two draw the same triple is $\frac1{64510\cdot256\cdot256}$, and the probability of this happening twice in succession is $\left(\frac1{64510\cdot256\cdot256}\right)^2$.

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I saw a similar problem here: askmehelpdesk.com/mathematics/… and people were talking about binomial distribution. Does this apply in my case? –  Halil Nov 25 '11 at 20:06
    
@Halil: Not as you’ve stated the problem, no. Yours is very straightforward. –  Brian M. Scott Nov 25 '11 at 20:28
    
Thank you Brian. –  Halil Nov 25 '11 at 21:18

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