Question

Italian gamblers used to bet on the total number of dots rolled on three six-sided dice. They believed the chance of rolling a nine ought to equal the chance of rolling a total of 10 since there were an equal number of different ways to get each sum. However, experience showed that these did not occur equally often. The gamblers asked Galileo for help with the apparent contradiction, and he resolved the paradox. Can you do the same? Be sure to explain both why the gamblers were confused and what the actual probabilities are. Include evidence from trials/simulations and theoretical calculations.

Answer 1

This is because theoretical probability of combinations and permutations are different. Through Combination the probability is 6/56 for both 9 and 10 however combinations are inaccurate due to the fact they count different combinations of numbers such as 1,2,3 and 3,2,1 as one probability when in fact they are different. Theoretical probability of permutations is different because it counts 1,2,3 and 3,2,1 as 2 instances. therefore the possible probability increases to 216 with 9 having a 25/216 chance and 10 having a 27/216 chance.

Answer 2

Eggbert/Kneegrow -- you are the same person. I see you're still trying to play games. You're skating close to the edge and are on the verge of being banned.