Question

two 6 - sided dice are rolled. what is the probability the sum of the two numbers on the die will be 9? (enter solution as a fraction) p(sum is 9) =

Explanation:

Step1: Find total number of outcomes

Each die has 6 sides. When two dice are rolled, by the fundamental counting principle, the total number of outcomes is $6\times6 = 36$.

Step2: Find favorable outcomes

The pairs of numbers on the two - dice that sum to 9 are $(3,6)$, $(4,5)$, $(5,4)$, $(6,3)$. So there are 4 favorable outcomes.

Step3: Calculate probability

The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P=\frac{4}{36}=\frac{1}{9}$.

Answer:

$\frac{1}{9}$