# 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 space. 2. What is the probability the sum of the...

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 space.

2. What is the probability the sum of the dice is nine?

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### 1 Answer

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**