Probability distribution of sum of three dice rolls

# probability distribution of sum of three dice rolls

import numpy as np
import matplotlib.pyplot as plt

N = 6
rng = range(1, N+1)  # range of dice numbers
MAX = 3 * N

counts = []
for total in range(MAX + 4):
    n = 0
    for i in rng:
        for j in rng:
            k = total - (i + j)
            if 0 < k <= N:
                n += 1
    counts.append((total, n))

# normalized probability distribution
dist = np.array(counts, dtype=float)
dist[:, 1] /= np.sum(dist[:, 1])

plt.plot(dist[:, 0], dist[:, 1], '+', lw=0, )
plt.show()