Question

In: Statistics and Probability

Create a simulation layout for rolling three dice 627 times. Calculate the probability of the three...

Create a simulation layout for rolling three dice 627 times. Calculate the probability of the three adding to 11.

Use Excel and show formulas used

Solutions

Expert Solution

here from excel ; we will create 3 columns(X1,X2,X3) for 3 dice rolls ; and use formula randbetween(1,6)

to have value between 1 to 6 in 627 cells in each category.

create another column Y =X1+X2+X3 to have sum of each row ;

below are the values

x1 x2 x3 y
3 5 3 11
1 6 5 12
2 6 3 11
6 5 6 17
2 1 6 9
3 3 1 7
2 5 2 9
6 5 2 13
5 5 6 16
2 6 5 13
3 2 3 8
3 2 5 10
6 1 3 10
6 2 5 13
1 2 4 7
4 6 1 11
1 6 3 10
5 3 1 9
2 1 2 5
2 3 2 7
4 6 4 14
6 3 2 11
3 4 2 9
4 6 6 16
4 2 2 8
2 5 3 10
2 3 3 8
3 5 5 13
6 3 1 10
5 3 5 13
1 3 6 10
2 5 4 11
3 1 3 7
6 5 4 15
6 5 2 13
2 4 2 8
1 1 5 7
2 4 5 11
4 6 3 13
2 3 6 11
3 6 3 12
6 2 5 13
6 5 1 12
3 3 6 12
6 5 2 13
2 5 3 10
5 3 3 11
5 2 1 8
5 4 6 15
1 4 5 10
5 6 3 14
1 5 6 12
2 3 2 7
1 1 4 6
4 2 6 12
5 5 5 15
3 3 1 7
3 3 3 9
6 4 1 11
6 1 2 9
6 5 4 15
5 4 4 13
5 4 1 10
4 3 4 11
3 6 1 10
3 5 2 10
3 6 3 12
6 4 4 14
6 3 3 12
1 5 5 11
4 1 4 9
1 5 2 8
4 3 5 12
3 1 1 5
2 2 3 7
5 1 2 8
2 3 2 7
6 2 1 9
6 4 2 12
4 1 3 8
1 4 6 11
2 4 1 7
5 2 3 10
3 6 2 11
5 2 3 10
4 6 5 15
4 2 5 11
5 4 3 12
2 6 3 11
6 2 4 12
4 2 6 12
4 5 2 11
3 3 5 11
1 4 1 6
1 1 1 3
2 5 1 8
3 1 4 8
4 2 3 9
4 5 2 11
2 5 5 12
5 1 2 8
6 2 2 10
3 2 5 10
1 3 2 6
1 4 1 6
5 1 4 10
3 3 3 9
6 1 5 12
5 6 2 13
2 2 5 9
2 3 2 7
2 5 3 10
2 3 4 9
1 2 5 8
2 6 5 13
3 6 4 13
3 3 4 10
2 5 5 12
3 4 3 10
6 3 4 13
6 3 1 10
4 4 4 12
1 2 2 5
1 6 3 10
4 4 5 13
3 1 3 7
5 1 2 8
6 4 1 11
6 3 4 13
3 4 4 11
5 5 1 11
6 1 4 11
2 4 6 12
6 3 1 10
4 2 4 10
2 6 2 10
6 3 6 15
1 2 6 9
6 1 4 11
5 4 6 15
5 3 5 13
4 2 4 10
1 5 3 9
3 6 5 14
6 3 3 12
6 3 4 13
6 6 6 18
6 4 1 11
2 4 6 12
1 2 2 5
4 2 1 7
4 5 3 12
4 6 2 12
4 1 3 8
5 1 5 11
1 2 5 8
2 3 1 6
3 1 3 7
4 5 5 14
3 2 4 9
5 2 6 13
6 6 4 16
2 6 2 10
5 5 3 13
1 4 5 10
5 6 3 14
5 6 1 12
3 1 5 9
3 2 1 6
1 1 4 6
3 3 2 8
2 3 4 9
6 2 6 14
5 1 1 7
3 4 3 10
1 3 3 7
6 6 2 14
2 3 1 6
1 3 2 6
4 5 3 12
1 3 1 5
1 3 5 9
2 1 6 9
6 6 4 16
2 6 2 10
2 4 6 12
2 3 5 10
6 4 4 14
6 4 5 15
3 1 6 10
3 4 5 12
4 1 2 7
6 5 4 15
6 1 5 12
6 1 5 12
4 1 4 9
6 3 1 10
1 1 2 4
2 2 6 10
3 6 2 11
1 5 4 10
4 5 6 15
5 4 4 13
1 4 3 8
6 2 2 10
4 6 5 15
4 1 5 10
1 5 5 11
1 1 2 4
5 5 5 15
4 6 3 13
1 2 5 8
5 5 1 11
6 3 6 15
4 2 4 10
6 4 4 14
2 1 6 9
1 4 1 6
4 5 3 12
2 6 1 9
2 5 6 13
2 1 3 6
1 1 2 4
1 5 6 12
2 5 2 9
2 6 6 14
6 2 6 14
4 6 6 16
2 5 5 12
3 6 4 13
4 6 4 14
4 3 2 9
4 6 5 15
3 6 5 14
1 5 3 9
3 6 3 12
2 5 4 11
1 2 6 9
5 3 3 11
6 5 3 14
1 3 4 8
4 5 1 10
3 3 2 8
4 3 1 8
5 6 4 15
1 3 1 5
5 6 1 12
2 1 5 8
6 5 4 15
1 3 2 6
2 5 3 10
6 2 6 14
3 3 1 7
5 1 1 7
4 4 5 13
6 5 6 17
4 3 4 11
4 6 5 15
5 1 4 10
5 2 4 11
5 5 5 15
2 4 1 7
3 3 6 12
6 1 1 8
4 2 4 10
3 5 1 9
4 3 2 9
6 4 1 11
2 6 4 12
5 2 6 13
6 2 1 9
3 1 6 10
4 2 5 11
4 5 2 11
2 1 3 6
1 5 2 8
6 6 5 17
4 3 6 13
5 5 4 14
4 4 5 13
4 6 5 15
2 2 3 7
5 3 2 10
3 3 2 8
6 1 3 10
6 4 4 14
2 2 3 7
3 5 3 11
6 1 3 10
6 4 2 12
3 4 6 13
6 4 3 13
5 5 3 13
1 5 6 12
6 6 2 14
1 5 4 10
5 3 2 10
4 2 4 10
6 5 6 17
4 6 6 16
6 3 3 12
5 4 3 12
3 3 6 12
3 5 4 12
6 1 4 11
4 5 1 10
6 4 5 15
3 4 4 11
5 6 1 12
1 5 1 7
6 6 1 13
4 4 6 14
1 4 2 7
6 6 1 13
1 1 1 3
4 5 6 15
3 6 5 14
1 5 2 8
6 1 3 10
5 2 4 11
4 5 4 13
2 6 1 9
5 4 3 12
3 5 1 9
2 2 6 10
5 6 2 13
4 4 1 9
6 4 5 15
5 2 2 9
1 4 2 7
5 2 2 9
1 4 3 8
5 3 5 13
6 5 5 16
1 5 1 7
5 6 6 17
5 6 5 16
4 1 4 9
3 1 6 10
3 2 3 8
1 5 6 12
1 4 6 11
3 1 2 6
4 6 5 15
6 2 3 11
2 2 5 9
4 3 1 8
1 1 4 6
1 4 6 11
6 3 3 12
5 5 6 16
4 1 6 11
6 4 2 12
6 2 2 10
3 1 4 8
1 3 4 8
6 1 1 8
4 4 3 11
1 2 2 5
6 3 1 10
3 4 6 13
5 6 2 13
2 1 1 4
2 4 3 9
4 4 2 10
2 1 3 6
2 1 1 4
6 2 3 11
6 4 4 14
6 1 3 10
4 1 4 9
5 3 5 13
1 1 1 3
4 1 1 6
6 1 5 12
5 6 5 16
4 5 1 10
1 1 3 5
5 5 2 12
3 4 3 10
6 1 5 12
1 5 1 7
1 2 1 4
2 2 3 7
1 5 3 9
6 5 2 13
5 1 6 12
2 6 3 11
1 4 6 11
4 5 1 10
3 4 1 8
3 2 5 10
1 1 5 7
6 1 6 13
6 1 1 8
5 2 1 8
2 4 4 10
5 6 3 14
6 2 1 9
4 6 3 13
1 2 4 7
2 5 3 10
5 6 1 12
1 5 3 9
1 3 1 5
6 3 1 10
4 3 1 8
3 6 6 15
1 4 4 9
3 2 3 8
4 2 6 12
1 6 5 12
3 6 4 13
1 1 2 4
1 5 1 7
6 4 6 16
3 5 5 13
1 3 2 6
3 3 1 7
6 4 1 11
2 6 1 9
4 4 4 12
2 1 2 5
1 1 6 8
1 2 6 9
6 4 2 12
2 3 5 10
6 6 3 15
3 2 5 10
3 2 1 6
5 2 1 8
1 3 1 5
5 2 6 13
2 1 6 9
4 4 6 14
1 3 6 10
4 2 6 12
2 3 3 8
1 6 5 12
3 5 6 14
2 5 4 11
4 5 5 14
6 1 6 13
3 2 2 7
5 3 6 14
6 2 3 11
4 3 3 10
4 3 6 13
6 6 6 18
2 5 3 10
1 1 3 5
1 5 2 8
4 3 6 13
5 3 3 11
5 2 6 13
2 3 4 9
4 6 3 13
1 5 1 7
5 5 1 11
3 1 5 9
3 1 5 9
5 3 5 13
4 6 5 15
4 5 5 14
5 5 5 15
3 1 1 5
3 5 3 11
6 2 2 10
5 3 6 14
5 5 1 11
6 4 5 15
4 1 2 7
4 4 5 13
1 1 6 8
1 6 4 11
5 4 3 12
6 5 2 13
3 2 1 6
1 4 5 10
2 4 5 11
6 2 1 9
1 5 1 7
3 6 4 13
2 1 2 5
3 6 4 13
5 3 2 10
3 5 4 12
1 4 5 10
2 3 6 11
2 2 4 8
2 6 1 9
5 2 3 10
5 3 4 12
6 2 2 10
4 3 1 8
3 5 1 9
5 6 2 13
4 2 6 12
6 1 4 11
3 2 2 7
2 1 6 9
6 2 4 12
1 4 2 7
1 5 4 10
6 6 2 14
1 3 6 10
2 3 3 8
4 3 1 8
6 6 3 15
1 1 2 4
6 2 3 11
2 5 3 10
3 4 2 9
5 4 5 14
3 1 4 8
5 5 5 15
5 6 1 12
2 3 6 11
6 5 6 17
5 1 6 12
3 5 5 13
5 3 5 13
5 6 2 13
2 1 2 5
3 3 3 9
5 3 1 9
5 4 4 13
1 4 6 11
5 4 5 14
6 3 1 10
1 3 6 10
2 1 3 6
5 2 3 10
5 4 3 12
2 6 2 10
6 5 4 15
2 3 5 10
4 2 3 9
6 6 1 13
4 2 6 12
6 6 4 16
1 5 3 9
4 6 5 15
5 2 3 10
3 5 2 10
1 6 5 12
6 6 3 15
3 1 1 5
3 6 2 11
6 5 3 14
2 6 2 10
2 6 3 11
3 3 3 9
3 4 6 13
6 5 2 13
5 6 3 14
5 4 1 10
2 3 4 9
5 2 3 10
1 2 1 4
3 3 1 7
3 2 1 6
6 1 1 8
2 1 3 6
6 3 2 11
3 1 4 8
5 1 2 8
5 5 2 12
1 3 4 8
6 4 5 15
2 3 5 10
5 3 5 13
2 4 3 9
2 1 3 6
2 3 4 9
6 2 5 13
2 2 5 9
6 5 4 15
2 4 4 10
4 1 3 8
5 5 1 11
2 3 4 9
4 3 3 10
1 4 5 10
5 4 5 14
5 5 1 11
6 2 6 14
6 2 3 11
4 6 6 16
2 1 1 4
3 1 5 9
3 2 6 11
3 1 1 5
1 3 1 5
1 2 5 8
1 3 5 9
3 4 2 9
3 5 3 11
1 4 6 11
2 4 4 10
2 6 6 14
2 5 5 12
6 3 5 14
6 5 6 17
5 5 6 16
2 4 1 7
1 6 1 8
1 4 3 8
6 2 1 9
1 5 5 11
5 4 4 13
5 6 1 12
2 2 2 6
4 1 1 6
2 4 6 12
4 2 4 10
1 3 1 5
6 3 4 13
6 2 3 11
4 2 3 9
4 3 5 12
3 1 4 8
6 2 1 9
5 6 3 14
4 4 5 13
6 3 5 14
6 2 2 10

from above :use countif formula in Y column to count number of times 11 appears ; in above simulation it appears 72 times

hence probability   of the three adding to 11 =72/627 =0.114833

(actual probability of 11 as a sum =27/216=0.125)


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