Question

Suppose you roll two dice. Find the number of elemnts in the event space of rolling sum of 9

Answer 1

whts event space?

Answer 2

A way to consider the entire sample space is to make a matrix with all the possible combinations of rolling 2 dice

Answer 3

let me see if I can get such a matrix up with this equation editor, basically on each edge you have the values of each die, 1 through 6, and in each cell you have the sum of values from each die

Answer 4

dicey matrix lol

1 2 3 4 5 6
1
2
3
4
5
6

Answer 5

\[\left[\begin{matrix} -& 1 & 2 & 3 & 4 & 5 & 6 \\ 1& 2 & 3 & 4 & 5 & 6 & 7 \\ 2& 3 & 4 & 5 & 6 & 7 & 8\\3& 4 & 5 & 6 & 7 & 8 & 9 \\4& 5 & 6 & 7 & 8 & 9 & 10\\5& 6 & 7 & 8 & 9 & 10 & 11\\6& 7 & 8 & 9 & 10 & 11 & 12\end{matrix}\right]\]

Answer 6

all righty now, in the first row that starts with the "-" you have the values of die #1, and in the first column that starts with "-" you have the values of die #2

Answer 7

Each cell represents (value of die #1) + (value of die #2), the only way to get 9 with two dice is to add \[3+6\] and \[4+5\]

Answer 8

because the values only range from 1 to 6, so you can see that given that there are only 2 ways to get 9 with values ranging from 1 to 6, then you have also have 2 dice, so you can have die#1=3 and die#2=6, and get 9, and then die#1=6 and die#2=3 and get 9, then die#1=4 and die#2=5 and get 9, and finally die#1=5 and die#2=4 and get 9

Answer 9

this is represented in the matrix at the bottom right corner

Answer 10

so what should i put for an answer?

Answer 11

well

Answer 12

how many ways can you get 9 with 2 dice? that is the answer...

Answer 13

the answer is in here: \[\left[\begin{matrix} -& 1 & 2 & 3 & 4 & 5 & 6 \\ 1& 2 & 3 & 4 & 5 & 6 & 7 \\ 2& 3 & 4 & 5 & 6 & 7 & 8\\3& 4 & 5 & 6 & 7 & 8 & 9 \\4& 5 & 6 & 7 & 8 & 9 & 10\\5& 6 & 7 & 8 & 9 & 10 & 11\\6& 7 & 8 & 9 & 10 & 11 & 12\end{matrix}\right]\]