A die is tossed twice. What is the probability of getting a sum of 10?

Options

A. `(1)/(18)`
B. `(1)/(6)`
C. `(1)/(12)`
D. `(5)/(12)`

Answer

To find the probability of getting a sum of 10 when a die is tossed twice, we can follow these steps:

### Step 1: Determine the Sample Space
When a die is tossed twice, each toss has 6 possible outcomes (1 through 6). Therefore, the total number of outcomes when tossing the die twice is:
\[ 6 \times 6 = 36 \]
This means the sample space consists of 36 possible outcomes.

**Hint:** Remember that the total outcomes for two independent events can be found by multiplying the number of outcomes for each event.

### Step 2: Identify the Favorable Outcomes
Next, we need to find the combinations of the two dice that result in a sum of 10. The possible combinations are:
- (4, 6)
- (5, 5)
- (6, 4)

These combinations give us a total of 3 favorable outcomes.

**Hint:** List all possible pairs (x, y) where x and y are the results of the two dice, and check which pairs add up to 10.

### Step 3: Calculate the Probability
The probability 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:
\[ P(\text{sum of 10}) = \frac{3}{36} = \frac{1}{12} \]

**Hint:** Simplify the fraction to find the final probability.

### Final Answer
The probability of getting a sum of 10 when a die is tossed twice is:
\[ \frac{1}{12} \]