The probability of getting a sum of 9 from two throws of a dice?

Options

A. `1/3`
B. `11/36`
C. `1/9`
D. `13/18`

Explanation

To find the probability of getting a sum of 9 from two throws of a dice, we can follow these steps:

### Step 1: Determine the Total Outcomes
When two dice are thrown, each die has 6 faces. Therefore, the total number of outcomes when throwing two dice is:
\[ 6 \times 6 = 36 \]

### Step 2: Identify the Favorable Outcomes
Next, we need to find all the combinations of the two dice that result in a sum of 9. The possible combinations are:
1. (3, 6)
2. (4, 5)
3. (5, 4)
4. (6, 3)

So, the favorable outcomes that give a sum of 9 are: (3, 6), (4, 5), (5, 4), and (6, 3). This gives us a total of 4 favorable outcomes.

### Step 3: Calculate the Probability
The probability \( P \) of an event is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ P(\text{sum of 9}) = \frac{4}{36} \]

### Step 4: Simplify the Probability
Now, we can simplify \( \frac{4}{36} \):
\[ P(\text{sum of 9}) = \frac{1}{9} \]

### Final Answer
Thus, the probability of getting a sum of 9 from two throws of a dice is:
\[ \frac{1}{9} \]

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