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pythonprobabilitydice

Probability - comparison 6-sided dices

I am in new probability. Please have me. We have 3 identical 6-sided dices. We role one dice first and the remaining 2 dices after that. What is the probability that the point obtained in the first roll is greater than the sum of points obtained in the second roll?

Solution

  • Since the total number of possibilities is quite small, 6**3, we can simply enumerate them all and count the number of events we are interested in:

    import itertools as IT

hits = 0
for roll in IT.product(range(1,7), repeat=3):
    if roll[0] > roll[1] + roll[2]:
        hits += 1
        print(roll, roll[1]+roll[2])
total = 6**3
print('Probability of first roll > sum of 2 rolls: {}/{} ~= {:.2%}'
      .format(hits,total,hits/total))

    reports

    Probability of first roll > sum of 2 rolls: 20/216 ~= 9.26%

    (Corrected based on Aniket Rangrej's solution).