Question

an experiment consists of rolling two fair dice and adding the dots on the two sides facing up. using the sample space provided below and assuming each simple event is as likely as any other, find the probability that the sum of the dots is less than 9. click the icon to view the sample space. the probability of getting a sum less than 9 is \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Total outcomes of two dice

Each die has 6 faces, so total outcomes = $6 \times 6 = 36$.

Step2: Count sums less than 9

Sums: 2(1),3(2),4(3),5(4),6(5),7(6),8(5). Total favorable = $1+2+3+4+5+6+5=26$.

Step3: Calculate probability

Probability = $\frac{\text{favorable}}{\text{total}} = \frac{26}{36} = \frac{13}{18}$.

Answer:

$\frac{13}{18}$