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 both numbers add up to one ?

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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,
$(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)$
Minimum sum of two dice is 2. So there is no outcomes which gives sum 1.
$P r o b a b i l i t y = \frac{d e s i r e d o u t c o m e s}{t o t a l o u t c o m e s}$
Probability = $\frac{0}{36} = 0$
So, the probability of the given question is $0$ .

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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 both numbers add up to one ?

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 both numbers add up to one ?