# Thread: Roll 2 Dice (2)

1. ## Roll 2 Dice (2)

2. If you roll 2 fair dice and add the points on each of the upturned face, what is the most likely sum? What is the probability of getting this sum?

Hint: For rolling 2 dice, there are 6 × 6 = 36 possible outcomes. You can write all 36 possible outcomes and find sum for each outcome, then find the probabilities of the sums. Or, alternatively, the number of ways of getting a particular sum ‘s’ can be found by expanding the ‘generating function’

g =(X+X^2+X^3+X^4+X^5+X^6)^2

and extracting the coefficient of X^5.

3. If you roll 3 fair dice and add the points on each of the upturned face, what is the most likely sum? What is the probability of getting this sum?
Hint: For rolling 3 dice, there are 6 × 6 × 6 = 216 possible outcomes. The number of ways of getting a particular sum ‘s’ can be found by expanding the ‘generating function’ g = (X+X^2+X^3+X^4+X^5+X^6)^3 and extracting the coefficient of X^5 .

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