Two fair dice are rolled. What is the probability of the dice being equal?
There are 6 possible outcomes for each dice roll, and since there are two dice, there are a total of 36 possible outcomes when both dice are rolled.
Out of these 36 outcomes, there are 6 outcomes where both dice have the same value: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).
Therefore, the probability of the dice being equal is 6/36, which simplifies to 1/6, or approximately 0.1667.
To calculate the probability of the two fair dice being equal, we first need to determine the total number of outcomes when rolling two dice.
Each die has six sides numbered from 1 to 6, so the total number of outcomes for a single die is 6.
Since we have two dice, we multiply the number of outcomes for each die together: 6 * 6 = 36.
Next, we need to determine the number of outcomes where the two dice are equal. There are six possible outcomes where the two dice show the same number: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).
Therefore, the probability of the dice being equal is the number of favorable outcomes (6) divided by the total number of possible outcomes (36):
P(equal dice) = 6/36 = 1/6.
Thus, the probability of rolling two fair dice and getting equal numbers is 1/6 or approximately 0.1667.
To find the probability of the dice being equal, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of outcomes when two fair dice are rolled. Each die has six sides, so there are 6 possible outcomes for each die. Since there are two dice, the total number of outcomes is 6 multiplied by 6, which equals 36.
Next, let's determine the number of favorable outcomes, which is the case when both dice show the same number. There are six possible outcomes in which both dice show the same number: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).
Therefore, the number of favorable outcomes is 6.
Finally, we can find the probability by dividing the number of favorable outcomes by the total number of outcomes:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 6 / 36
Simplifying the fraction, we get:
Probability = 1 / 6
So, the probability of the dice being equal is 1/6 or approximately 0.1667.