Bill and Jane play a simple game involving two fair dice, each of which has six sides numbered from \(1\) to \(6\) (with an equal chance of landing on any side). Bill rolls the dice and his score is the total of the two dice. Jane then rolls the dice and her score is the total of her two dice. If Jane’s score is higher than Bill’s, she wins the game. What is the probability the Jane will win the game?

(A) \(\dfrac{15}{36}\)

(B) \(\dfrac{175}{432}\)

(C) \(\dfrac{575}{1296}\)

(D) \(\dfrac{583}{1296}\)

(E) \(\dfrac12\)

Answer: C

Source: Manhattan GMAT