question_answer

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:

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 \[=\frac{8}{16}=\frac{1}{2}\]