> barplot(dbinom(0:12,12,1/6),names.arg=c(0:12),space=0,xlab="Sum of Dice",ylab="Probability",main="Prob. Distribution of the Sum under H0",col="papayawhip")
> data.frame(list(Sum = 0:12, Prob = round(dbinom(0:12,12,1/6),10)))
   Sum         Prob
1    0 0.1121566548
2    1 0.2691759715
3    2 0.2960935686
4    3 0.1973957124
5    4 0.0888280706
6    5 0.0284249826
7    6 0.0066324959
8    7 0.0011369993
9    8 0.0001421249
10   9 0.0000126333
11  10 0.0000007580
12  11 0.0000000276
13  12 0.0000000005
> 
> 
> R1 = c(8:12)
> sum(dbinom(R1,12,1/6))
[1] 0.0001555443
> R2 = c(5:12)
> sum(dbinom(R2,12,1/6))
[1] 0.03635002
> 
> R3 = c(4:12)
> sum(dbinom(R3,12,1/6))
[1] 0.1251781
> R4 = c(4,6)
> sum(dbinom(R4,12,1/6))
[1] 0.09546057
> sum(dbinom(c(7:12),12,1/6))
[1] 0.001292544
> for(i in 1:13){pvals[i] = binom.test(i-1,12,p=1/6,alternative="two.sided")$p.value}
> pvals
[[1]]
[1] 0.2373347

[[2]]
[1] 0.7039064

[[3]]
[1] 1

[[4]]
[1] 0.4347305

[[5]]
[1] 0.1251781

[[6]]
[1] 0.03635002

[[7]]
[1] 0.00792504

[[8]]
[1] 0.001292544

[[9]]
[1] 0.0001555443

[[10]]
[1] 1.341935e-05

[[11]]
[1] 7.860225e-07

[[12]]
[1] 2.802301e-08

[[13]]
[1] 4.593937e-10

>