If a number $x$ is chosen from the numbers 1,2,3 and a number $y$ is chosen from the numbers 1,2,3 and a number is chosen from the numbers 4,5,6, then the probability of product of $x$ is chosen from the numbers 4,5,6, then the probability of product of and $y$ and less than 12 is

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Detailed Solution

According to the question, a number x is selected from the numbers 1,2,3 and then a second number y is chosen from the numbers 4,5,6.
Number x can be selected in 3 ways and corresponding to each such way there are 3 ways of selecting number y, so the two numbers can be selected in

3 \times 3 =

9 ways.
Sample space = {(1,4), (1,5), (1,6), (2,4), (2,5), (2,6), (3,4), (3,5), (3,6)}
Total number of outcomes = 9.
The product xy will be less than 12 if, (1,4), (1,5), (1,6), (2,4), (2,5) are chosen.
Number of favorable outcomes = 5.
Hence, the probability that the product xy is less than 12