MathProbabilityEvents and probabilities

Formal definition of probability

Galileo's riddle

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If we roll three dice at the same time, we can get a sum of 9 or 10 in six ways:
$10 = 1 + 3 + 6 = 1 + 4 + 5 = 2 + 2 + 6 = 2 + 3 + 5 = 2 + 4 + 4 = 3 + 3 + 4$ $9 = 1 + 2 + 6 = 1 + 3 + 5 = 1 + 4 + 4 = 2 + 2 + 5 = 2 + 3 + 4 = 3 + 3 + 3$

So, one would think that the probabilities of getting 9 and 10 are equal. But Galileo knew about the long experience of dice players, which showed that the result of 10 was more likely. Eventually, Galileo explained this mystery. Try to find the correct explanation!

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The rearrangements of the dice should be taken into account. For example, 2+4+4 and 4+2+4 are actually different outcomes if 2 comes out on different dice

The dice are always slightly unfair, and this gives an advantage for the sum of 10

The dice players' observations and their estimates of probabilities were inaccurate

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