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 :
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Step-by-Step Solution
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.