Question

1. you roll two fair 6 - sided dice and add the numbers. what is the probability you roll a sum that is 4 or less?

Explanation:

Step1: Calculate total number of outcomes

When rolling two 6 - sided dice, the total number of outcomes is $n(S)=6\times6 = 36$ (by the fundamental counting principle).

Step2: Find number of favorable outcomes

The possible sums that are 4 or less:

• Sum of 2: $(1,1)$ (1 outcome)
• Sum of 3: $(1,2),(2,1)$ (2 outcomes)
• Sum of 4: $(1,3),(2,2),(3,1)$ (3 outcomes)

The number of favorable outcomes $n(A)=1 + 2+3=6$.

Step3: Calculate probability

Using the probability formula $P(A)=\frac{n(A)}{n(S)}$, we substitute $n(A) = 6$ and $n(S)=36$. So $P(A)=\frac{6}{36}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$