If you have two pairs of six-sided fair dice, two people total each rolls their pair simulatenously, what's the probability one's sum >other's sum etc

GRE Quant Problem Solving
1

If you have two pairs of six-sided fair dices, two people total each rolls the pair simultaneously,

  1. what’s the probability one’s sum >other’s sum .
  2. what’s the probability at least one single die of one person exceeds the sum of both of the other’s dice?
  3. what’s the probability either single die of one person exceeds the sum of both of the other’s dice?

Since all dice are identical, isn’t the probability one half for question one.

2

https://math.stackexchange.com/questions/4739535/if-you-have-two-pairs-of-six-sided-fair-dice-two-people-total-each-rolls-their

The comment is correct.