Excellent in math, poor in math, excellent in physics total score of 5 2 7, poor in physics score of 1 12 13, and total score of 61420 (ii) Propose the hypothesis that students' math scores have nothing to do with physics scores. According to the contingency table above, we can get K2=20×(5× 12? 1× 2) 26×14× 7×13 ≈ 8.802 > 7.879. When H0 holds, the probability of K2 > 7.879 is about 0.005, where 8.802 > 7.879.

So we are 99.5% sure that students' math scores are related to their physics scores.

(3) The number 12 includes (2,6), (4,6), (3,4) and (4,3).

There are 36 basic events (1, 1) (1, 2)( 1, 3)( 1, 4)( 1, 5) (1,

(2, 1)(2,2),(2,3),(2,4),(2,5)(2,6)

(3, 1)(3,2),(3,3),(3,4),(3,5)(3,6)

(4, 1)(4,2),(4,3),(4,4),(4,5)(4,6)

(5, 1)(5,2),(5,3),(5,4),(5,5)(5,6)

(6, 1)(6,2),(6,3),(6,4),(6,5)(6,6)

Therefore, the winning probability of 12 is p = 436 = 19.