How do I answer the following? I have no understanding of probability!Two dice are rolled. The sum of the values are recorded. 1. Define the sample...

We have two regular 6-sides
dice.

Then, we know that each die has the outcomes (1, 2,
3, 4, 5, or, 6)

Now we rolled 2
dice.

We need to find the sample
space.

The sample space is all possible outcomes of the
event.

In this example, the sample space is obtained from
the sum of the numbers on both dice.

Possible outcomes
are:

(1+1) = 2

(1+2) = (2+1)=
3

(2+3) = (3+2)= (1+4) = (4+1)=
5

(3+3) = (2+4) = (4+2) = (1+5) = (5+1) =
6

(3+4) = (4+3) = (2+5) = (5+1) = (1+6) = (6+1) =
7

(4+4) = (5+3) = (3+5) ...... =
8

(5+4) = (4+5) .............=
9

(6+4) = (4+ 6) .............=
10

(5+6) = (6+5) ...............=
11

(6+6) =
12

1)Then, we conclude that the sample space
is { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12 }

Now we need to determine the
probability of having a sum of 9.

We know that all possible
outcomes are 6*6 = 36 possible outcome.

Now we need to
determine the possibility of getting a sum of 9.

To get a
sum of 9 we need to get the followsing outcomes.

==>
(4+5) ,  (5+4) ,  ( 3+6) ,or (6+3)

The total is 4
pairs.

2. Then the probability is 4/36 =
1/9