help me understand probability case work

i've been trying to calculate the probability of winning. and here what i came up.

x my roll add 2 meaning X = 1 => 3

y friend roll

x roll p(x > y|X=x) p(X=x) p( x > y |y n X = x)

1 = 3 2/8 1/6 2/48

2 = 4 3/8 1/6 3/48

3 = 5 4/8 1/6 4/48

4 = 6 5/8 1/6 5/48

5 = 7 6/8 1/6 6/48

6 = 8 7/8 1/6 7/48

(sorry for the weird format, tried to do a table)

which adds up to 27/48 = 0.5625

but in the solution they say 7/12

what am i missing in my case work?

thanks.

Note by Tay Ko
10 months, 3 weeks ago

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