Combinatorics, probability, dice
- by TarGz
A friend of mine asked: if I have two dice and I throw both of them, what is the most frequent sum (of the two dice' numbers)?
I wrote a small script:
from random import randrange
d = dict((i, 0) for i in range(2, 13))
for i in xrange(100000):
d[randrange(1, 7) + randrange(1, 7)] += 1
print d
Which prints:
2: 2770,
3: 5547,
4: 8379,
5: 10972,
6: 13911,
7: 16610,
8: 14010,
9: 11138,
10: 8372,
11: 5545,
12: 2746
The question I have, why is 11 more frequent than 12? In both cases there is only one way (or two, if you count reverse too) how to get such sum (5 + 6, 6 + 6), so I expected the same probability..?
