SOLUTION: Consider a die with eight sides marked one,two,three, and so. Assuming equally likely outcome,find the probability that the sum of two dice is the given number. Enter the answer ei

Question 487189: Consider a die with eight sides marked one,two,three, and so. Assuming equally likely outcome,find the probability that the sum of two dice is the given number. Enter the answer either as a fraction or as a decimal,round to three places
a:P(4)=
b:P(6)=
c:(10)=
d:P(11)=
e:P(14)=
f:P(16)=
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!


You must make a chart for the sample space of all possible
dice throws:
 
Here is the sample space. It contains 64 possible outcomes:

(1,1)  (1,2)   (1,3)  (1,4)   (1,5)  (1,6)  (1,7)  (1,8)

(2,1)  (2,2)   (2,3)  (2,4)   (2,5)  (2,6)  (2,7)  (2,8)

(3,1)  (3,2)   (3,3)  (3,4)   (3,5)  (3,6)  (3,7)  (3,8)

(4,1)  (4,2)   (4,3)  (4,4)   (4,5)  (4,6)  (4,7)  (4,8)

(5,1)  (5,2)   (5,3)  (5,4)   (5,5)  (5,6)  (5,7)  (5,8)

(6,1)  (6,2)   (6,3)  (6,4)   (6,5)  (6,6)  (6,7)  (6,8)

(7,1)  (7,2)   (7,3)  (7,4)   (7,5)  (7,6)  (7,7)  (7,8)

(8,1)  (8,2)   (8,3)  (8,4)   (8,5)  (8,6)  (8,7)  (8,8)

You'll find that all throws with a given sum are on a diagonal.

-----------------------------------
a:P(4)
The throws with sum 4 are in red:

(1,1)  (1,2)   (1,3)  (1,4)   (1,5)  (1,6)  (1,7)  (1,8)

(2,1)  (2,2)   (2,3)  (2,4)   (2,5)  (2,6)  (2,7)  (2,8)

(3,1)  (3,2)   (3,3)  (3,4)   (3,5)  (3,6)  (3,7)  (3,8)

(4,1)  (4,2)   (4,3)  (4,4)   (4,5)  (4,6)  (4,7)  (4,8)

(5,1)  (5,2)   (5,3)  (5,4)   (5,5)  (5,6)  (5,7)  (5,8)

(6,1)  (6,2)   (6,3)  (6,4)   (6,5)  (6,6)  (6,7)  (6,8)

(7,1)  (7,2)   (7,3)  (7,4)   (7,5)  (7,6)  (7,7)  (7,8)

(8,1)  (8,2)   (8,3)  (8,4)   (8,5)  (8,6)  (8,7)  (8,8)

Therefore P(4) is 3 out of 64 or 

-------------------------------------------------
b:P(6)
The throws with sum 6 are in red:


(1,1)  (1,2)   (1,3)  (1,4)   (1,5)  (1,6)  (1,7)  (1,8)

(2,1)  (2,2)   (2,3)  (2,4)   (2,5)  (2,6)  (2,7)  (2,8)

(3,1)  (3,2)   (3,3)  (3,4)   (3,5)  (3,6)  (3,7)  (3,8)

(4,1)  (4,2)   (4,3)  (4,4)   (4,5)  (4,6)  (4,7)  (4,8)

(5,1)  (5,2)   (5,3)  (5,4)   (5,5)  (5,6)  (5,7)  (5,8)

(6,1)  (6,2)   (6,3)  (6,4)   (6,5)  (6,6)  (6,7)  (6,8)

(7,1)  (7,2)   (7,3)  (7,4)   (7,5)  (7,6)  (7,7)  (7,8)

(8,1)  (8,2)   (8,3)  (8,4)   (8,5)  (8,6)  (8,7)  (8,8)

Therefore P(6) is 5 out of 64 or 

-------------------------------------------------

The throws with sum 10 are in red:

(1,1)  (1,2)   (1,3)  (1,4)   (1,5)  (1,6)  (1,7)  (1,8)

(2,1)  (2,2)   (2,3)  (2,4)   (2,5)  (2,6)  (2,7)  (2,8)

(3,1)  (3,2)   (3,3)  (3,4)   (3,5)  (3,6)  (3,7)  (3,8)

(4,1)  (4,2)   (4,3)  (4,4)   (4,5)  (4,6)  (4,7)  (4,8)

(5,1)  (5,2)   (5,3)  (5,4)   (5,5)  (5,6)  (5,7)  (5,8)

(6,1)  (6,2)   (6,3)  (6,4)   (6,5)  (6,6)  (6,7)  (6,8)

(7,1)  (7,2)   (7,3)  (7,4)   (7,5)  (7,6)  (7,7)  (7,8)

(8,1)  (8,2)   (8,3)  (8,4)   (8,5)  (8,6)  (8,7)  (8,8)

Therefore P(10) is 7 out of 64 or 

-------------------------------------------------

The throws with sum 11 are in red:

(1,1)  (1,2)   (1,3)  (1,4)   (1,5)  (1,6)  (1,7)  (1,8)

(2,1)  (2,2)   (2,3)  (2,4)   (2,5)  (2,6)  (2,7)  (2,8)

(3,1)  (3,2)   (3,3)  (3,4)   (3,5)  (3,6)  (3,7)  (3,8)

(4,1)  (4,2)   (4,3)  (4,4)   (4,5)  (4,6)  (4,7)  (4,8)

(5,1)  (5,2)   (5,3)  (5,4)   (5,5)  (5,6)  (5,7)  (5,8)

(6,1)  (6,2)   (6,3)  (6,4)   (6,5)  (6,6)  (6,7)  (6,8)

(7,1)  (7,2)   (7,3)  (7,4)   (7,5)  (7,6)  (7,7)  (7,8)

(8,1)  (8,2)   (8,3)  (8,4)   (8,5)  (8,6)  (8,7)  (8,8)

Therefore P(11) is 6 out of 64 or  which reduces to 

-------------------------------------------------

The throws with sum 14 are in red:

(1,1)  (1,2)   (1,3)  (1,4)   (1,5)  (1,6)  (1,7)  (1,8)

(2,1)  (2,2)   (2,3)  (2,4)   (2,5)  (2,6)  (2,7)  (2,8)

(3,1)  (3,2)   (3,3)  (3,4)   (3,5)  (3,6)  (3,7)  (3,8)

(4,1)  (4,2)   (4,3)  (4,4)   (4,5)  (4,6)  (4,7)  (4,8)

(5,1)  (5,2)   (5,3)  (5,4)   (5,5)  (5,6)  (5,7)  (5,8)

(6,1)  (6,2)   (6,3)  (6,4)   (6,5)  (6,6)  (6,7)  (6,8)

(7,1)  (7,2)   (7,3)  (7,4)   (7,5)  (7,6)  (7,7)  (7,8)

(8,1)  (8,2)   (8,3)  (8,4)   (8,5)  (8,6)  (8,7)  (8,8)

Therefore P(14) is 3 out of 64 or 

-------------------------------------------------

The throw with sum 16 is in red:

(1,1)  (1,2)   (1,3)  (1,4)   (1,5)  (1,6)  (1,7)  (1,8)

(2,1)  (2,2)   (2,3)  (2,4)   (2,5)  (2,6)  (2,7)  (2,8)

(3,1)  (3,2)   (3,3)  (3,4)   (3,5)  (3,6)  (3,7)  (3,8)

(4,1)  (4,2)   (4,3)  (4,4)   (4,5)  (4,6)  (4,7)  (4,8)

(5,1)  (5,2)   (5,3)  (5,4)   (5,5)  (5,6)  (5,7)  (5,8)

(6,1)  (6,2)   (6,3)  (6,4)   (6,5)  (6,6)  (6,7)  (6,8)

(7,1)  (7,2)   (7,3)  (7,4)   (7,5)  (7,6)  (7,7)  (7,8)

(8,1)  (8,2)   (8,3)  (8,4)   (8,5)  (8,6)  (8,7)  (8,8)

Therefore P(16) is 1 out of 64 or 

-------------------------------------------------
Edwin

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