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A large jug contains 2018 nickels and 2019 dimes.  Next to the jug is a large...

A large jug contains 2018 nickels and 2019 dimes.  Next to the jug is a large pile of dimes (treat it as an unlimited number of dimes).  The following procedure is to be performed repeatedly until a single coin remains in the jug. 

Two coins are chosen at random from the jug:

i.  If both coins are dimes, one is put back and the other is discarded.

ii.  If both coins are nickels, both are discarded and a dime from the pile is added to the jug. 

iii.  If one coin is a dime and the other is a nickel, the nickel is put back and the dime is discarded.            
Will the last coin remaining in the jug be a nickel or a dime?

Math   Statistics-And-Probability   
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