Three dice

All possible sums from rolling three dice

set.seed(1234)
sort(sample(3:18, size=16, replace=F, prob=c(1/216, 3/216, 6/216, 10/216, 15/216, 21/216, 25/216, 27/216, 27/216, 25/216, 21/216, 15/216, 10/216, 6/216, 3/216, 1/216)))

##  [1]  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18

The frequency of sums for rolling three dice 100000 times.

data <- sort(sample(3:18, size=100000, replace=T, prob=c(1/216, 3/216, 6/216, 10/216, 15/216, 21/216, 25/216, 27/216, 27/216, 25/216, 21/216, 15/216, 10/216, 6/216, 3/216, 1/216)))

table(data)

## data
##     3     4     5     6     7     8     9    10    11    12    13    14    15 
##   474  1415  2779  4685  6885  9616 11689 12520 12485 11454  9708  7108  4566 
##    16    17    18 
##  2747  1411   458

as.data.frame(table(data))

##    data  Freq
## 1     3   474
## 2     4  1415
## 3     5  2779
## 4     6  4685
## 5     7  6885
## 6     8  9616
## 7     9 11689
## 8    10 12520
## 9    11 12485
## 10   12 11454
## 11   13  9708
## 12   14  7108
## 13   15  4566
## 14   16  2747
## 15   17  1411
## 16   18   458

Histogram for the sum of three dice

dice1 <- sample(1:6, 100000, T)  
dice2 <- sample(1:6, 100000, T)
dice3 <- sample(1:6, 100000, T)
hist(dice1+dice2+dice3)

This is an empirical histogram. It is the sum of rolling three dice for 100000 times.