Find the probability of getting a sum of 9 or 10 in a throw of two dice.

Explanation

To find the probability of getting a sum of 9 or 10 when throwing two dice, we can follow these steps:

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

### Step 2: Find the number of outcomes for a sum of 9
Next, we need to find all the combinations of the two dice that result in a sum of 9. The possible pairs are:
- (3, 6)
- (4, 5)
- (5, 4)
- (6, 3)

Counting these, we find there are 4 combinations that yield a sum of 9.

### Step 3: Calculate the probability of getting a sum of 9
The probability of getting a sum of 9 is given by the number of favorable outcomes divided by the total number of outcomes:
\[ P(\text{sum} = 9) = \frac{\text{Number of ways to get 9}}{\text{Total outcomes}} = \frac{4}{36} = \frac{1}{9} \]

### Step 4: Find the number of outcomes for a sum of 10
Now, we find the combinations that result in a sum of 10. The possible pairs are:
- (4, 6)
- (5, 5)
- (6, 4)

Counting these, we find there are 3 combinations that yield a sum of 10.

### Step 5: Calculate the probability of getting a sum of 10
The probability of getting a sum of 10 is:
\[ P(\text{sum} = 10) = \frac{\text{Number of ways to get 10}}{\text{Total outcomes}} = \frac{3}{36} = \frac{1}{12} \]

### Step 6: Combine the probabilities
To find the total probability of getting a sum of either 9 or 10, we add the two probabilities together:
\[ P(\text{sum} = 9 \text{ or } 10) = P(\text{sum} = 9) + P(\text{sum} = 10) = \frac{4}{36} + \frac{3}{36} = \frac{7}{36} \]

### Final Answer
The probability of getting a sum of 9 or 10 when throwing two dice is:
\[ \frac{7}{36} \]

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