From the first set "x" can be selected in 3 ways and from the next set "y" can be selected in 3 ways. So, there are 9 ways to select a pair (x,y) from both the sets. 

Problem:
A number x is selected from the numbers 1, 2, 3 and then a second number y is randomly selected from the numbers 1, 4, 9. What is the probability that the product xy of the two numbers will be less than 9?

Solution:

To find the probability that the product xy will be less than 9, we need to determine the possible combinations of x and y that satisfy this condition and calculate the ratio of favorable outcomes to the total number of outcomes.

Step 1: List all possible outcomes
To find the total number of outcomes, we need to list all possible combinations of x and y.

The possible values of x are 1, 2, and 3, and the possible values of y are 1, 4, and 9. Therefore, the total number of outcomes is 3 * 3 = 9.

Step 2: Determine favorable outcomes
We need to find the combinations of x and y that satisfy the condition xy < />

We can create a table to list all possible combinations of x and y and calculate their products:

| x | y | xy |
|---|---|----|
| 1 | 1 | 1 |
| 1 | 4 | 4 |
| 1 | 9 | 9 |
| 2 | 1 | 2 |
| 2 | 4 | 8 |
| 2 | 9 | 18 |
| 3 | 1 | 3 |
| 3 | 4 | 12 |
| 3 | 9 | 27 |

From the table above, we can see that there are 4 combinations of x and y where the product xy is less than 9: (1, 1), (1, 4), (1, 9), and (2, 1).

Step 3: Calculate the probability
The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of outcomes.

In this case, the number of favorable outcomes is 4 and the total number of outcomes is 9.

Therefore, the probability that the product xy will be less than 9 is given by:

P(xy < 9)="favorable" outcomes="" total="" outcomes="4" />

Answer:
The probability that the product xy will be less than 9 is 4/9.