To explain NinjaAnswer's answer:
Of the three dice rolled, one may match the original pair and two are different, and this can occur three ways: ( 1/6 x 5/6 x 5/6 ) + ( 5/6 x 1/6 x 5/6 ) + ( 5/6 x 5/6 x 1/6 ) = 75/216
[ where 1/6 is the probability of matching the first two and 5/6 is the probability of not matching the first two ]
Or, two may match the original pair and one is different:
( 1/6 x 1/6 x 5/6 ) + ( 1/6 x 5/6 + 1/6 ) + ( 5/6 x 1/6 x 1/6 ) = 15/216
Or, all three may match the original pair: ( 1/6 x 1/6 x 1/6 ) = 1/216
Or, all three may be the same, but not match the original pair:
( 5/6 x 1/6 x 1/6 ) = 5/216
[ where 5/6 is the probability of getting a new number and 1/6 is the probability of matching that new number ]
Adding these together: 75/216 + 15/216 + 1/216 + 5/216 = 96/216 = 4/9
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