If two dice are tossed, find the probability of throwing a total of ten or more.

Options

A. `1/6`
B. `1/3`
C. `1/4`
D. `2/3`

Answer

To find the probability of throwing a total of ten or more when two dice are tossed, we can follow these steps:

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

### Step 2: Identify Favorable Outcomes
Next, we need to find the combinations of the two dice that result in a total of 10 or more. The possible sums that are 10 or more are 10, 11, and 12.

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

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

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

Now, let's count these combinations:
- For a sum of 10: 3 combinations
- For a sum of 11: 2 combinations
- For a sum of 12: 1 combination

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

### Step 3: Calculate the Probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{6}{36} = \frac{1}{6} \]

### Final Answer
Thus, the probability of throwing a total of ten or more when two dice are tossed is:
\[ \frac{1}{6} \]

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