If two different dice are rolled together, the probability of getting an even number on both dice, is:
$ (A)\ \frac{1}{36}$
$( B) \ \frac{1}{2}$
$( C) \ \frac{1}{6}$
$ ( D) \ \frac{1}{4} \ $

Given: If two different dice are rolled together

To do: the probability of getting an even number on both dice

Solution: Possible outcomes on rolling the two dice are given below:

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

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

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

Total number of outcomes $=36$

Favourable outcomes are given below:

{$( 2,\ 2) ,\ ( 2,\ 4) ,\ ( 2,\ 6) ,\ ( 4,\ 2) ,\ ( 4,\ 4) ,\ ( 4,\ 6) ,\ ( 6,\ 2) ,\ ( 6,\ 4) ,\ ( 6,6)\}$

Total number of favourable outcomes $=9$

Probability of getting an even number on both dice $=\frac{Total\ number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}$

$=\frac{9}{36}$

$=\frac{1}{4}$

Hence, the correct option is $( D)$.

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Updated on: 10-Oct-2022

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