A number is chosen from the numbers 1, 2, 3 and denoted as x, and a number is chosen from the numbers 1, 4, 9 and denoted as y. Then P(xy < 9) is :

Step 1: List all possible outcomes

First, we need to determine all possible pairs $(x,y)$ that can be formed by choosing one number from the set $\{1, 2, 3\}$ for $x$ and one number from the set $\{1, 4, 9\}$ for $y$. This set of all possible pairs is called the sample space, denoted by $S$.

Step 2: Calculate the total number of outcomes

To find the total number of possible outcomes, we multiply the number of choices for $x$ by the number of choices for $y$. This gives us the size of our sample space.

Step 3: Identify favorable outcomes

Next, we identify the outcomes where the product $xy$ is less than 9. These are the favorable outcomes for the event $E$. We list all such pairs from our sample space.

Step 4: Calculate the number of favorable outcomes

By counting the pairs identified in the previous step, we find the total number of favorable outcomes, denoted as $n(E)$.

Step 5: Calculate the probability

Finally, the probability of the event $E$ (where $xy < 9$) is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

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