To determine the probability of rolling two six-sided dice and obtaining a pair of sixes, we can follow a straightforward approach.
Each die has six faces, numbered from 1 to 6. When rolling two dice, each die operates independently of the other, meaning the outcome of one die does not affect the other. The total number of possible outcomes when rolling two dice can be calculated by multiplying the number of faces on the first die by the number of faces on the second die:
Total Outcomes = 6 (faces on die 1) x 6 (faces on die 2) = 36 possible combinations
Now, let’s identify the favorable outcomes for our scenario. The only way to roll a pair of sixes is if both Dice 1 and Dice 2 show a 6. Therefore, there is only one favorable outcome:
Favorable Outcomes = 1 (rolling a 6 on Die 1 and a 6 on Die 2)
To find the probability of this event occurring, we use the formula for probability:
Probability = (Number of Favorable Outcomes) / (Total Number of Outcomes)
Plugging in our numbers gives:
Probability = 1 / 36
Thus, the probability of rolling two six-sided dice and obtaining a 6 and a 6 is approximately 0.0278 or 2.78%.
This means that if you were to roll two dice many times, you could expect to roll a pair of sixes about 2.78% of the time.