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, then the probability that the product x y of the two numbers will be less than 9 is

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Detailed Solution

Given, 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.
The probability of an event to be occurred is the division of the number of favourable outcomes by the total number of outcomes that is,

Probability of an event = Number of favourable cases Total number of cascs

Find the total number of possible outcomes.
The numbers x and y can be selected three and three ways as, (1, 1), (1, 4), (1, 9), (2, 1), (2, 4), (2, 9), (3, 1), (3, 4) and (3, 9).
So, the total number of possible outcomes is 9.
Find the number of favourable outcomes.
The product

x y

is less than 9 if the two numbers are selected in the following ways, (1, 1), (1, 4), (2, 1), (2, 4) and (3, 1).
So, the number of favourable outcomes is 5.
Find the required probability: by using the formula of probability that is,