Find the (theoretical) probability of a given event, assuming that the dice are distinguishable and fair, and that what is observed are numbers uppermost.

Two dice are rolled; the numbers add to 7.
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Out of 36 possibilities, 7 = 4&3, 3&4, 2&5, 5&2, 6&1 or 1&6. Each has a probability of 1/36.

To find the "either-or" probability, add the individual probabilities.

P = 6/36 = 1/6

To find the probability of the event where the sum of the numbers rolled on two dice is 7, we need to determine the number of favorable outcomes (outcomes where the sum is 7) and divide it by the total number of possible outcomes.

Step 1: Determine the number of favorable outcomes:
When rolling two dice, there are six possible outcomes for each dice, ranging from 1 to 6. To get a sum of 7, we can have the following combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). So the number of favorable outcomes is 6.

Step 2: Determine the total number of possible outcomes:
When rolling two dice, each dice has 6 possible outcomes. Since the dice are distinguishable, we multiply the number of outcomes of the first dice (6) by the number of outcomes of the second dice (6) to get the total number of possible outcomes. So the total number of possible outcomes is 6*6 = 36.

Step 3: Calculate the probability:
Now that we have the number of favorable outcomes (6) and the total number of possible outcomes (36), we can calculate the probability of the event. Probability is defined as the number of favorable outcomes divided by the total number of outcomes.

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 6 / 36
Probability = 1/6

Therefore, the theoretical probability of rolling two dice and getting a sum of 7 is 1/6.