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} enter the denominator of your simplified fraction

Explanation:

Step1: Count all outcomes

When rolling two dice, each die has 6 possible outcomes. So the total number of outcomes when rolling two dice is \(6\times6 = 36\) since for each outcome of the first - die, there are 6 outcomes of the second die.

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 \(P=\frac{\text{Desired Outcomes}}{\text{All Outcomes}}=\frac{6}{36}=\frac{1}{6}\). We are asked for the denominator of the simplified fraction.

Answer:

6