It's easy to duplicate random draws with replicate (here's an example of ten replications):
Rep <- replicate(10, sample(1:10, 3))
Rep
5 |
7 |
6 |
6 |
1 |
4 |
10 |
7 |
8 |
10 |
7 |
10 |
4 |
10 |
6 |
8 |
2 |
1 |
2 |
8 |
8 |
2 |
5 |
2 |
3 |
9 |
1 |
4 |
1 |
9 |
Your inequality's empirical probability can be determined as follows:
set.seed(1222)
Rep <- replicate(100, sample(1:10, 3))
prob1 <- mean(reps[1, ] + reps[2, ] > reps[3, ] * 2)
prob1
0.39
We can produce all 1,000 potential combinations of x1, x2, and x3 just to be sure, because there are only 1,000 possible possibilities.
all.prob <- expand.grid(1:10, 1:10, (1:10) * 2)
probs <- mean(all.probs[,1] + all.probs[,2] > all.probs[,3])
probs
0.475