To determine the probability of getting a sum of 6 when rolling a 6-sided die twice, we first need to identify all the possible outcomes when rolling the die twice. Each roll has 6 possible outcomes since it's a 6-sided die.
The sum of 6 can be achieved in the following ways:
1. Rolling a 1 on the first die and a 5 on the second die.
2. Rolling a 2 on the first die and a 4 on the second die.
3. Rolling a 3 on the first die and a 3 on the second die.
4. Rolling a 4 on the first die and a 2 on the second die.
5. Rolling a 5 on the first die and a 1 on the second die.
Therefore, there are 5 favorable outcomes that result in a sum of 6 when rolling the die twice.
Since each die has 6 sides, there are a total of 6 * 6 = 36 possible outcomes when rolling the die twice.
The probability (P) of getting a sum of 6 can be calculated as:
P(sum of 6) = Number of favorable outcomes / Total number of possible outcomes
P(sum of 6) = 5 favorable outcomes / 36 possible outcomes
P(sum of 6) = 5/36
Therefore, the probability of getting a sum of 6 when rolling a 6-sided die twice is 5/36 or five thirty-sixths.
