Two standard dice are rolled, what is the probability of rolling a pair (both the same number)?

We note that, if a die is rolled the sample space:

`S={1,2,3,4,5,6}`

We know that ,if two dice rolled the sample space :

`S={1,2,3,4,5,6}xx{1,2,3,4,5,6}`

`:.S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),`
`color(white)(...............)(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),`
`color(white)(...............)(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),`
`color(white)(...............)(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),`
`color(white)(...............)(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),`
`color(white)(...............)(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}`

i.e. When two dice are tossed together ,

the possible pairs are : `color(blue)(n=6xx6=36`

Let ,event `E=`the same number on both dice.

`=> E={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}`

`=>`no. of comeout pair `color(blue)( r=6`

So , the probability of rolling the pair `=P(E)=r/n`

`=>P(E)=6/36`

`=>P(E)=1/6~~0.17`

Since we are rolling two six-sided dice, there are `6xx6`, or `36` different possibilities. This will be our denominator.

How many ways can we get double numbers?

`{1,1}, {2,2}, {3,3}, {4,4}, {5,5}, {6,6}`

We have `6` different ways of getting double numbers. This is our numerator.

Thus, the probability of rolling pairs is `6/36` or

`1/6`

Hope this helps!