Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is less than $9$.

Given: Two dice are thrown at the same time and the product of numbers appearing on them is noted.

To do: To find the probability that the product is less than $9$.

As given that two dice are rolled.

Then the probability of outcomes $n( S)=6\times6=36$.

Let E be the event of getting a product less than $9$.

The number whose product is less than $9$ 

$=( 1,\ 1),\ ( 1,\ 2),\ ( 1,\ 3),\ ( 1,\ 4),\ ( 1,\ 5),\ ( 1,\ 6),\ ( 2,\ 1),\ ( 2,\ 2),\ ( 2,\ 3),\ ( 2,\ 4),\ ( 3,\ 1),\ ( 3,\ 2),\ ( 4,\ 1),\ ( 4,\ 2),\ ( 5,\ 1),\ ( 6,\ 1)$

$=16$

Therefore the required probability

$P( E)=\frac{n( E)}{n( S)}$

$=\frac{16}{36}$

$=\frac{4}{9}$.