To calculate the probability of rolling two fair six-sided dice and getting the same number on both, we start by identifying the total possible outcomes and the favorable outcomes.
When rolling two dice, each die can land on one of 6 faces (numbered from 1 to 6). Therefore, the total number of possible outcomes when rolling two dice is:
6 (for Die 1) x 6 (for Die 2) = 36 total outcomes.
Now, for the event where both dice show the same number, we can have the following pairs:
- (1,1)
- (2,2)
- (3,3)
- (4,4)
- (5,5)
- (6,6)
This gives us a total of 6 favorable outcomes.
Therefore, the probability of both dice showing the same number is calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Possible Outcomes = 6 / 36 = 1 / 6.
Thus, the probability of rolling two fair six-sided dice and getting the same number on both is 1/6.