Two dice having six sides with numbers $1, 2, 3, 4, 5$ and $6$ written on them or rolled. Answer the questions that follow.
What is the probability that the two dice show up the same number ?

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Solution

Let’s figure out the number of possible outcomes. Each has $6$ possible outcomes $(1, 2, 3, 4, 5, 6)$ , so the combination of these two becomes $6 \times 6 = 36$ .
Below the first number in the parenthesis is the outcome of the first die and the second number is the outcome of the second die.
Now, of these $36$ possible combinations, how many show the same number? Six of them:
$(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)$
$(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)$
$(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)$
$(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)$
$(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)$
$(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)$
$P r o b a b i l i t y = \frac{d e s i r e d o u t c o m e s}{t o t a l o u t c o m e s}$
Probability = $\frac{6}{36} = \frac{1}{6}$
So, the probability of the given question is $\frac{1}{6}$ .

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Two dice having six sides with numbers 1,2,3,4,5 and 6 written on them or rolled. Answer the questions that follow. What is the probability that the two dice show up the same number ?

Two dice having six sides with numbers $1, 2, 3, 4, 5$ and $6$ written on them or rolled. Answer the questions that follow.
What is the probability that the two dice show up the same number ?