# Probability of 2 people drawing same A and same B

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.
(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 $\left(\frac1{64510\cdot256\cdot256}\right)^2$.