Question

if you rolled two dice, what is the probability that you would roll a sum of 8?
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 outcomes. So the total number of outcomes is \(6\times6 = 36\) (using the multiplication principle \(n = n_1\times n_2\), where \(n_1=n_2 = 6\)).

Step2: Count the number of outcomes with sum 8

The pairs \((x,y)\) such that \(x + y=8\) (where \(x\) is the result of the first die and \(y\) is the result of the second die) are \((2,6)\), \((3,5)\), \((4,4)\), \((5,3)\), \((6,2)\). So there are 5 desired outcomes.

Step3: Calculate the probability

Using the formula \(P=\frac{\text{Desired Outcomes}}{\text{All Outcomes}}\), we substitute the values. \(P=\frac{5}{36}\)

Answer:

5