A number $x$ is selected at random from the numbers 1,2,3 and 4. Another number $y$ is selected at random from the numbers 1,4, 9 and 16. Find the probability that product of $x$ and $y$ is less than 16.

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Detailed Solution

Given, a number

x

is selected at random from the numbers 1,2,3 and 4. Another number

y

is selected at random from the numbers 1,4, 9 and 16.
The probability of an event occurring is calculated by dividing the number of favourable outcomes by the total number of outcomes, that is,

Probability of an cvent = Number of favourable outcomes Total number of outcomes

Find the total number of possible outcomes by selecting the numbers x and y in the following ways,
(1, 1), (1. 4), (1, 9), (1, 16), (2, 1), (2, 4), (2, 9), (2, 16), (3, 1), (3, 4), (3, 9), (3, 16), (4, 1), (4, 4), (4, 9) and (4, 16).
So, the total number of possible outcomes is 16.
Find the number of favourable outcomes.
Given that the product of numbers is less than 16.
Consequently, the positive results are (1, 1), (1, 4), (1, 9), (2, 1), (2, 4), (3, 1), (3, 4) and (4, 1).
Thus, the number of favourable outcomes is 8.
Find the required probability by dividing the number of favourable outcomes by the total number of outcomes that is, 8 and 16 respectively.