If you roll two fair six-sided dice, what is the probability that the dice show the same number?
6 doubles out of 36 possible throws, so ...
Look at the matrix of outcomes of tossing two dice.
there are 6 cases where the numbers are the same, e.g. (4,4)
so
prob(your event) = 6/36 = 1/6
To find the probability that the two dice show the same number when rolled, we can start by determining the total number of possible outcomes.
When rolling one six-sided die, there are six equally likely outcomes: 1, 2, 3, 4, 5, and 6. Since there are two dice being rolled, we need to calculate the total number of outcomes for two dice.
In total, there are 6 possible outcomes for the first die and 6 possible outcomes for the second die. To find the total number of outcomes when rolling two dice, we multiply the number of outcomes for the first die (6) by the number of outcomes for the second die (6), resulting in 6 x 6 = 36 total outcomes.
Now, let's determine the favorable outcomes, which are the outcomes where the two dice show the same number. For instance, if both dice show a 1, that would be considered a favorable outcome. The same is true for any other number: (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6).
Since there are 6 favorable outcomes (one for each number on the die), the probability of rolling two dice and getting the same number is 6 favorable outcomes out of 36 possible outcomes.
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which in this case is 6.
Thus, the simplified fraction becomes 1/6.
Therefore, the probability of rolling two fair six-sided dice and getting the same number is 1/6.