URGENT HELP MATHS

Forthe red die (R) :
Pr(R=6) = (1/3)
Pr(R=1) = Pr(R=2) = Pr(R=3) = Pr(R=4) = Pr(R=5) = [1 - (1/3)]/5 = 2/15

For the white die (W) :
Pr(W=1) = Pr(W=2) = Pr(W=3) = Pr(W=4) = Pr(W=5) = Pr(W=6) = 1/6

Consider when the red die wins :
Pr(R=2 and W=1) = (2/15) × (1/6) = 1/45
Pr(R=3 and W≤2) = (2/15) × (2/6) = 2/45
Pr(R=4 and W≤3) = (2/15) × (3/6) = 3/45
Pr(R=5 and W≤4) = (2/15) × (4/6) = 4/45
Pr(R=6 and W≤5) = (1/3) × (5/6) = 5/18

Pr(the red die wins)
= (1/45) + (2/45) + (3/45) + (4/45) + (5/18)
= 1/2

Pr(the white die wins)
= 1 - (1/2)
= 1/2

2015-01-21 05:06:32 補充：
Pr(the red die wins) = Pr(the white die wins)
Both dice have equal chances to win.

P(r = 6) = 1/3
P(r = 1) = P(r = 2) = ... = (1 - 1/3)/5 = 2/15
P(w = 1) = P(w = 2) = ... = 1/6

P(red win)
= P(r = 6, w < 6) + P(r = 5, w < 5) + ... + P(r = 2, w < 2)
= (1/3)(5/6) + (2/15)(4/6 + 3/6 + 2/6 + 1/6)
= 1/2

Choosing which dice doesn't matter... maybe I've made a mistake again XD