220 If we roll two dice and observe the sum the most common

2.20 If we roll two dice and observe the sum, the most common outcome is 7 and occurs with probability 1/6. But what if we roll more than 2 dice? (a) Suppose we roll three dice and observe the sum. What is the most likely sum and what is the probability of its occurrence? (b) Repeat part (a) for the case of four dice?

If we roll more than 2 dice

outcomes would be 3, 4, .......18

The sum repeats along diagonals.

Diagonal max length = 6

Prob for sum =9 = 12/216

    the sample space is as below:  (1,1,1)  (1,1,2)  (1,1,3)  (1,1,4)  (1,1,5)  (1,1,6)  (1,2,1)  (1,2,2)  (1,2,3)  (1,2,4)  (1,2,5)  (1,2,6)  (1,3,1)  (1,3,2)  (1,3,3)  (1,3,4)  (1,3,5)  (1,3,6)  (1,4,1)  (1,4,2)  (1,4,3)  (1,4,4)  (1,4,5)  (1,4,6)  (1,5,1)  (1,5,2)  (1,5,3)  (1,5,4)  (1,5,5)  (1,5,6)  (1,6,1)  (1,6,2)  (1,6,3)  (1,6,4)  (1,6,5)  (1,6,6)  (2,1,1)  (2,1,2)  (2,1,3)  (2,1,4)  (2,1,5)  (2,1,6)  (2,2,1)  (2,2,2)  (2,2,3)  (2,2,4)  (2,2,5)  (2,2,6)  (2,3,1)  (2,3,2)  (2,3,3)  (2,3,4)  (2,3,5)  (2,3,6)  (2,4,1)  (2,4,2)  (2,4,3)  (2,4,4)  (2,4,5)  (2,4,6)  (2,5,1)  (2,5,2)  (2,5,3)  (2,5,4)  (2,5,5)  (2,5,6)  (2,6,1)  (2,6,2)  (2,6,3)  (2,6,4)  (2,6,5)  (2,6,6)  (3,1,1)  (3,1,2)  (3,1,3)  (3,1,4)  (3,1,5)  (3,1,6)  (3,2,1)  (3,2,2)  (3,2,3)  (3,2,4)  (3,2,5)  (3,2,6)  (3,3,1)  (3,3,2)  (3,3,3)  (3,3,4)  (3,3,5)  (3,3,6)  (3,4,1)  (3,4,2)  (3,4,3)  (3,4,4)  (3,4,5)  (3,4,6)  (3,5,1)  (3,5,2)  (3,5,3)  (3,5,4)  (3,5,5)  (3,5,6)  (3,6,1)  (3,6,2)  (3,6,3)  (3,6,4)  (3,6,5)  (3,6,6)  (4,1,1)  (4,1,2)  (4,1,3)  (4,1,4)  (4,1,5)  (4,1,6)  (4,2,1)  (4,2,2)  (4,2,3)  (4,2,4)  (4,2,5)  (4,2,6)  (4,3,1)  (4,3,2)  (4,3,3)  (4,3,4)  (4,3,5)  (4,3,6)  (4,4,1)  (4,4,2)  (4,4,3)  (4,4,4)  (4,4,5)  (4,4,6)  (4,5,1)  (4,5,2)  (4,5,3)  (4,5,4)  (4,5,5)  (4,5,6)  (4,6,1)  (4,6,2)  (4,6,3)  (4,6,4)  (4,6,5)  (4,6,6)  (5,1,1)  (5,1,2)  (5,1,3)  (5,1,4)  (5,1,5)  (5,1,6)  (5,2,1)  (5,2,2)  (5,2,3)  (5,2,4)  (5,2,5)  (5,2,6)  (5,3,1)  (5,3,2)  (5,3,3)  (5,3,4)  (5,3,5)  (5,3,6)  (5,4,1)  (5,4,2)  (5,4,3)  (5,4,4)  (5,4,5)  (5,4,6)  (5,5,1)  (5,5,2)  (5,5,3)  (5,5,4)  (5,5,5)  (5,5,6)  (5,6,1)  (5,6,2)  (5,6,3)  (5,6,4)  (5,6,5)  (5,6,6)  (6,1,1)  (6,1,2)  (6,1,3)  (6,1,4)  (6,1,5)  (6,1,6)  (6,2,1)  (6,2,2)  (6,2,3)  (6,2,4)  (6,2,5)  (6,2,6)  (6,3,1)  (6,3,2)  (6,3,3)  (6,3,4)  (6,3,5)  (6,3,6)  (6,4,1)  (6,4,2)  (6,4,3)  (6,4,4)  (6,4,5)  (6,4,6)  (6,5,1)  (6,5,2)  (6,5,3)  (6,5,4)  (6,5,5)  (6,5,6)  (6,6,1)  (6,6,2)  (6,6,3)  (6,6,4)  (6,6,5)  (6,6,6)

2.20 If we roll two dice and observe the sum, the most common outcome is 7 and occurs with probability 1/6. But what if we roll more than 2 dice? (a) Suppose w

220 If we roll two dice and observe the sum the most common

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