Directions: Study the table and answer the question that follows.

The table gives the total number of notebooks sold by five stationery counters on a particular day, along with the ratio of hardcover notebooks to softcover notebooks sold by each counter.

Stationery Counters	Total Notebooks Sold	Hardcover Notebooks : Softcover Notebooks
A	135	5:4
B	140	9:5
C	180	4:5
D	160	13:19
E	150	7:8

When two fair dice are rolled together, what is the probability that their total is 7 or that both dice display the same number?

The correct answer is $\frac{1}{3}$.

Note: The table regarding stationery counters and notebook sales is independent data and is not required to solve this probability question.

Step 1: Determine the total number of possible outcomes when two fair dice are rolled.
Each fair six-sided die has faces numbered 1 through 6. When two dice are rolled simultaneously, the total number of possible outcomes is:

$\text{Total Outcomes}=6\times 6=36$

Step 2: Find the favorable outcomes for Event A (Total sum is 7).
The combinations of numbers on the two dice that sum up to 7 are:
(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
The number of favorable outcomes for Event A is:

$n\left(A\right)=6$

Step 3: Find the favorable outcomes for Event B (Both dice display the same number).
The pairs where both dice show identical numbers (doubles) are:
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
The number of favorable outcomes for Event B is:

$n\left(B\right)=6$

Step 4: Check for overlapping outcomes (Event A and Event B).
Because 7 is an odd number, no pair of identical numbers can add up to 7 (since the sum of any two equal integers is always even). Therefore, Events A and B are mutually exclusive, meaning they share no outcomes in common:

$n(A\cap B)=0$

Step 5: Calculate the total number of favorable outcomes.
The total number of favorable outcomes for getting a total of 7 OR both dice displaying the same number is:

$n(A\cup B)=n\left(A\right)+n\left(B\right)=6+6=12$

Step 6: Calculate the required probability.
The probability of an event is given by the ratio of favorable outcomes to total possible outcomes:

$P(A\cup B)=\frac{n(A\cup B)}{\text{Total Outcomes}}=\frac{12}{36}=\frac{1}{3}$

Thus, the required probability is $\frac{1}{3}$.