6. Toss a pair of dice. What is the probability that the sum is twenty or six?

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UpStudy AI · Accepted Answer

To solve the problem, we need to determine the probability of rolling a sum of either 20 or 6 with a pair of dice.

### Step 1: Analyze the possible outcomes
When tossing a pair of six-sided dice, the possible sums range from 2 (1+1) to 12 (6+6). Therefore, a sum of 20 is impossible with two dice.

### Step 2: Calculate the probability of rolling a sum of 6
Next, we need to find the combinations that result in a sum of 6. The possible pairs (die1, die2) that yield a sum of 6 are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)

This gives us a total of 5 combinations that result in a sum of 6.

### Step 3: Calculate the total number of outcomes
The total number of outcomes when rolling two dice is:
$$
6 \times 6 = 36
$$

### Step 4: Calculate the probability
The probability $$ P $$ of rolling a sum of 6 is given by the ratio of the number of favorable outcomes to the total number of outcomes:
$$
P(\text{sum of 6}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{5}{36}
$$

### Final Answer
Since a sum of 20 is impossible, the probability of getting a sum of 20 or 6 is simply the probability of getting a sum of 6:
$$
P(\text{sum of 20 or 6}) = P(\text{sum of 6}) = \frac{5}{36}
$$

Thus, the final answer is:
$$
\frac{5}{36}
$$
The probability of rolling a sum of 6 is $$ \frac{5}{36} $$.

6. Toss a pair of dice. What is the probability that the sum is twenty or six?

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