To solve this problem, we need to find the probability that the product of two dice is less than 9. Let's break down the problem into smaller steps:

Step 1: Determine the sample space
When two dice are thrown simultaneously, the possible outcomes for each die are 1, 2, 3, 4, 5, and 6. Since there are two dice, the sample space consists of all possible pairs of numbers that can be obtained from the two dice. Therefore, the sample space contains 6 x 6 = 36 possible outcomes.

Step 2: Determine the favorable outcomes
We need to find the pairs of numbers whose product is less than 9. Let's list all the pairs:

1 x 1 = 1
1 x 2 = 2
1 x 3 = 3
1 x 4 = 4
1 x 5 = 5
1 x 6 = 6
2 x 1 = 2
2 x 2 = 4
2 x 3 = 6
2 x 4 = 8
3 x 1 = 3
3 x 2 = 6
4 x 1 = 4
5 x 1 = 5
6 x 1 = 6

From this list, we can see that there are 14 favorable outcomes where the product is less than 9.

Step 3: Determine the probability
The probability of an event happening is given by the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the number of favorable outcomes is 14 and the total number of possible outcomes is 36. Therefore, the probability of the product being less than 9 is:

Probability = 14 / 36 = 7 / 18

However, this is not one of the options given in the question. To find the correct option, we need to simplify the fraction 7/18.

Step 4: Simplify the fraction
To simplify the fraction 7/18, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 7 and 18 is 1.

Dividing 7 by 1 gives 7, and dividing 18 by 1 gives 18. Therefore, the simplified fraction is:

7 / 18

Now we can compare this fraction with the options given in the question.

Option A: 1/36
Option B: 4/9
Option C: 17/36
Option D: 2/9

The simplified fraction 7/18 does not match any of the options exactly. However, we can see that 4/9 is the closest option to 7/18. Therefore, the correct answer is option B: 4/9.

Total number of outcomes = 36