Two dice are rolled simultaneously . Find the probability of getting a sum greater than 9.

Options

A. `10/11`
B. `5/6`
C. `1/6`
D. `8/9`

Answer

To find the probability of getting a sum greater than 9 when two dice are rolled, we can follow these steps:

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

### Step 2: Identify the outcomes that result in a sum greater than 9.
We need to find all the combinations of the two dice that yield sums greater than 9. The possible sums greater than 9 are 10, 11, and 12.

- **Sum = 10**:
- (4, 6)
- (5, 5)
- (6, 4)

- **Sum = 11**:
- (5, 6)
- (6, 5)

- **Sum = 12**:
- (6, 6)

Now, let's count these outcomes:
- For a sum of 10, we have 3 outcomes.
- For a sum of 11, we have 2 outcomes.
- For a sum of 12, we have 1 outcome.

Adding these gives us:
\[ 3 + 2 + 1 = 6 \text{ favorable outcomes} \]

### Step 3: Calculate the probability.
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability \( P \) of getting a sum greater than 9 is:
\[ P(\text{sum} > 9) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{36} \]

### Step 4: Simplify the probability.
Now we simplify the fraction:
\[ \frac{6}{36} = \frac{1}{6} \]

### Final Answer:
The probability of getting a sum greater than 9 when two dice are rolled is:
\[ \frac{1}{6} \]

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