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

Number of possible outcomes for $x$ is $1,2,3,4=4$

Number of possible outcomes for $y$ is $1,4,9,16=4$

Since they are selected at random, hence each has equal in number of possibilities.

Therefore, total outcomes $=16$ (like a dice question making a box and writing the products as
$(1\times 1),(1\times 4),(1\times 9),(1\times 16),(2\times 1),(2\times 4),(2\times 9),(2\times 16),(3\times 1),(3\times 4),(3\times 9),(3\times 16),$
$(4\times 1),(4\times 4),(4\times 9),(4\times 16)$

Favourable outcomes $=8.$

$(1\times 1),(1\times 4),(1\times 9),(2\times 1),(2\times 4)(3\times 1),(3\times 4),$$(4\times 1)$

Probability that product of $x$ and $y$ is less than $16=$ $\frac{8}{16}=\frac{1}{2}$