When rolling a 6-sided die twice, the possible outcomes for the sum of the rolls range from 2 to 12. Let's calculate the probability of getting a sum of 2 or 5.

1. Probability of getting a sum of 2:

• The only way to get a sum of 2 is by rolling a 1 on both dice: $(1,1)$.
• There is 1 favorable outcome.

2. Probability of getting a sum of 5:

• To get a sum of 5, the following outcomes are possible: $(1,4), (2,3), (3,2), (4,1)$.
• There are 4 favorable outcomes.

Total Possible Outcomes:

• Since each die has 6 faces, and they are rolled independently, the total number of possible outcomes is $6 \times 6 = 36$.

Calculating Probabilities:

• Probability of getting a sum of 2: $\frac{1}{36}$.
• Probability of getting a sum of 5: $\frac{4}{36} = \frac{1}{9}$.

Combined Probability:

To find the probability of getting either a sum of 2 or a sum of 5, we add these probabilities:

$\text{Combined Probability} = \frac{1}{36} + \frac{4}{36} = \frac{5}{36}$

So, the probability of getting a sum of either 2 or 5 is $\frac{5}{36}$.

Would you like more details or have any questions?

Here are five related questions:

1. What is the probability of getting a sum of 7 or 11 when rolling two 6-sided dice?
2. How do you calculate the probability of getting a specific sum with two dice?
3. What is the probability of getting a sum of 8 with two 6-sided dice?
4. How does the probability distribution of sums change with more dice?
5. What are the most likely sums when rolling two 6-sided dice, and why?

Tip: When calculating probabilities for dice rolls, consider all possible combinations of dice that result in the desired outcome.