Question

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.

Answer 1

Let x be 1, 2, 3 or 4

and y be 1, 4, 9 or 16.

Now, $xy=\{1,4,9,16,2,8,18,32,3,12,27,48,4,16,36,64\}$

Total number of possible outcomes = 16

Number of outcomes where product is less than 16

= 8

i.e., $\{1,4,9,2,8,3,12,4\}$

$\therefore$ Required probability = $\frac{8}{16}=\frac{1}{2}$