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If we throw three dice at the same time and see a sum of numbers. What number will have the greatest probability. I think that that number is 11 but I am not positive. Any help will be appreciated.

Community
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Milingona Ana
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3 Answers3

5

Possible Sums with three dice are 3 ... 18

3 -> 1+1+1 Possible Combinations: 1

4 -> 1+2+1 Possible Combinations:3

5 -> (1+3+1),(1,2,2) Possible Combinations:6

6 -> (1,4,1), (1,3,2),(2,2,2) Possible Combinations:10

7 -> (1,4,2), (1,3,3),(5,1,1),(3,2,2) Possible Combinations:15

8 -> (1,4,3) , (1,2,5) ,(1,1,6),(4,2,2),(3,3,2) Possible Combinations:21

9 -> (6,2,1) , (5,3,1) ,(5,2,2), (4,4,1) ,(4,3,2),(3,3,3) Possible Combinations:25

10 -> (6,3,1) , (6,2,2) , (5,3,2), (5,4,1), (4,4,2),(4,3,3) Possible Combinations:27

11 -> (6,4,1),(6,3,2),(5,5,1),(5,4,2) (5,3,3),(4,4,3) Possible Combinations:27

12 -> (6,5,1),(6,4,2), (6,3,3),(5,5,2),(5,4,3),(4,4,4) Possible Combinations:25

13 -> (6,6,1) ,(6,5,2),(6,4,3),(5,5,3),(5,4,4) Possible Combinations:21

14 -> (6,4,4),(6,5,3),(5,5,4),(6,6,2) Possible Combinations::15

15-> (6,6,3),(6,4,5),(5,5,5) Possible Combinations:10

16-> (6,6,4),(6,5,5) Possible Combinations:6

17-> (6,6,5) Possible Combinations3

18-> 6,6,6 Possible Combinations:1

Hence the answer is 10,11

demented hedgehog
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Max
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10 and 11 both have the highest probability. The short explanation is that there are an even number of possible outcomes (3-18) and the probabilities are highest in the middle and get lower as you move to the extremes. The middle two values are 10 and 11.

(BTW, "dices" in incorrect: "dice" is plural already. To refer to just one, the word is "die.")

James Jensen
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Hint: Consider only one die and try to think of which number appears the most as a sum of two numbers of the die. It is $7=1+6=2+5=3+4$. Agree? You try to pick the kind of "middle ones" to get your sum.

Metin Y.
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