To find the probability of rolling two dice twice and getting a sum of 6 both times, we can approach this step by step.

Step 1: Probability of getting a sum of 6 on one roll of two dice

When rolling two six-sided dice, the total number of possible outcomes is $6 \times 6 = 36$. To get a sum of 6, the following pairs of dice rolls can occur:

• (1, 5)
• (2, 4)
• (3, 3)
• (4, 2)
• (5, 1)

These are 5 favorable outcomes.

Thus, the probability of rolling a sum of 6 on one roll is: $P(\text{sum of 6 on one roll}) = \frac{5}{36}$

Step 2: Probability of getting a sum of 6 on both rolls

Since the events are independent, the probability of rolling a sum of 6 twice in a row is the product of the probabilities of getting a sum of 6 on each roll.

$P(\text{sum of 6 on both rolls}) = \frac{5}{36} \times \frac{5}{36} = \frac{25}{1296}$

Thus, the probability of rolling two dice twice and getting a sum of 6 both times is $\frac{25}{1296}$, or approximately 0.0193.

Would you like more details or have any other questions?

Here are 5 related questions:

1. What is the probability of rolling a sum of 7 on two dice twice?
2. What is the probability of rolling a double (e.g., two 4s) twice in a row?
3. How does the probability change if you roll three dice and want a sum of 6?
4. How many total combinations give a sum of 8 when rolling two dice?
5. What is the probability of not getting a sum of 6 on either of the two rolls?

Tip: When calculating probabilities for multiple independent events, remember to multiply the probabilities of each individual event.