If two dice are rolled simultaneously, what is the probability that the number is the same on both dice?
You are really asking:
After you throw the first one and have some number from 1 to 6,
what is the probability that the next one will get that number?
1/6
To find the probability that the number on both dice is the same when they are rolled simultaneously, we need to determine the number of favorable outcomes (when the numbers on both dice are the same) and divide it by the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes:
When two dice are rolled simultaneously, there are six possible outcomes for each dice (since each dice has six sides numbered from 1 to 6). For the favorable outcomes, we need to find the combination of numbers that match. There are six combinations: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).
Step 2: Determine the total number of possible outcomes:
Since each dice has six possible outcomes, the total number of possible outcomes when both dice are rolled is 6 * 6 = 36.
Step 3: Calculate the probability:
To find the probability, divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
In this case, the number of favorable outcomes is 6, and the total number of possible outcomes is 36.
Probability = 6 / 36 = 1 / 6
So, the probability that the number is the same on both dice is 1/6, which is approximately 0.167 or 16.7%.