Question

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

Answer 1

Let $x=1⟹y<16$

Probability of $xy$ is less than $16$ is $\frac{3}{4^2}$

Let $x=2⟹y<8$

Probability of $xy$ is less than $16$ is $\frac{2}{4^2}$

Let $x=3⟹y<\frac{16}{3}$

Probability of $xy$ is less than $16$ is $\frac{2}{4^2}$

Let $x=4⟹y<4$

Probability of $xy$ is less than $16$ is $\frac{1}{4^2}$

Total Probability of $xy$ is less than $16$ is $\frac{3}{16}+\frac{2}{16}+\frac{2}{16}+\frac{1}{16}=\frac{1}{2}$