Question

if you rolled two dice, what is the probability that you would roll two of the same number?
second
first 1 2 3 4 5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
probability = \frac{desired outcome}{all outcomes}
simplify your fraction, then enter the numerator.

Explanation:

Step1: Count all possible outcomes

When rolling two dice, each die has 6 possible values. So the total number of outcomes is $6\times6 = 36$.

Step2: Count desired outcomes

The desired outcomes (rolling two - of the same number) are $(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)$, which is 6 outcomes.

Step3: Calculate probability

The probability $P=\frac{\text{Desired Outcomes}}{\text{All Outcomes}}=\frac{6}{36}=\frac{1}{6}$.
The problem asks for the numerator of the simplified fraction, which is 1.

Answer:

1