What is the probability of rolling two dice twice getting a sum of 6 both times?


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.

What is the probability of rolling two dice twice getting a sum of 6 both times?

Explore the probability of rolling two dice twice and getting a sum of 6 both times. This problem involves key concepts in probability, including independent events and combinatorics. Suitable for students in Grades 8-10, the solution breaks down the formula and provides a step-by-step explanation.

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