# Two dice are thrown. Find probability of the number on the face of the second die being greater than the number of the upper face of the first die ?

##### 2 Answers

#### Explanation:

this can be done very simply by using symmetry

it can be done in many ways, one of them is

the total permutations this can take which are the number of ways we can get a unique ordered pair are

out of which since there are 6 sides, we will have 6 cases in which both of the die show the same value

therefore number of ways in which the two die show different values are

therefore the chance of getting different numbers on the dice are

Now we can use symmetry, the fact that the probability that the number on the first dice is greater then the number on the second die is equal to the probability that the number on the second dice is greater than the first (Just switch up the die!)

therefore

=

which on simplifying becomes

=

#### Explanation:

Note that the order of the dice is specified, so you can consider the desirable outcomes on the second die if the outcome of the first die is known:

If the first die shows

If the first die shows

If the first die shows

The probability of any number on the first doe is