Two dice arc rolled once. Find the probability of getting such numbers on the two dice, whose product is 12.

Given: Two dice.

To do: To find the probability of getting such numbers on the both dice, whose product is 12, when two dice are rolled.

When two dice are rolled, there are 36 total possible outcomes

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

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

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

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

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

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

Product of outcomes will be 12 for

$( 2,6) ,\ ( 6,2) ,\ ( 3,4)$ and $( 4,3)$

No. of favourable outcomes $=4\ $

Probability $=\frac{no.\ of\ favourable\ outcomes}{total\ no.\ of\ possible\ outcomes}=\frac{4}{36} =\frac{1}{9}$

Thus, $\frac{1}{9}$ is the probability of getting such numbers on the both dice, whose product is 12, when two dice are rolled.