A die has six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and total scores are recorded.
What is the probability of getting a total of 7?

Answer

To solve the problem of finding the probability of getting a total of 7 when two dice with faces marked 0, 1, 1, 1, 6, and 6 are thrown together, 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 outcomes when throwing two dice is calculated as:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]

### Step 2: Identify the possible outcomes that give a total of 7
Next, we need to find all the combinations of the two dice that result in a total score of 7. The possible pairs from the two dice are:
- (1, 6)
- (6, 1)

Now, let's analyze these pairs:
1. **(1, 6)**: This can occur in three ways since the die has three faces marked with 1:
- (1 from die 1, 6 from die 2)
- (1 from die 1, 6 from die 2)
- (1 from die 1, 6 from die 2)

Thus, we have 3 combinations for (1, 6).

2. **(6, 1)**: Similarly, this can also occur in three ways:
- (6 from die 1, 1 from die 2)
- (6 from die 1, 1 from die 2)
- (6 from die 1, 1 from die 2)

Thus, we also have 3 combinations for (6, 1).

### Step 3: Calculate the total favorable outcomes
Now, we sum the favorable outcomes:
- From (1, 6): 3 outcomes
- From (6, 1): 3 outcomes

Total favorable outcomes = 3 + 3 = 6.

### Step 4: Calculate the probability
The probability of getting a total of 7 is given by the ratio of the number of favorable outcomes to the total number of outcomes:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{6}{36} = \frac{1}{6} \]

### Final Answer
Thus, the probability of getting a total of 7 when two such dice are thrown is:
\[ \frac{1}{6} \]

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