Question

If a dice is rolled four times what is the probability that the same number is rolled at least twice? Round your answer to four decimal places and show your work.

Answer 1

`(171)/(1296)`

Explanation:

Let’s try to go this way.

For example the number is k. It can be of course any number. So k is between 1 to 6.

The chance of rolling exactly zero ks is:
`((5)/(6)) ^(4)`=625/1296;

The chance of rolling exactly one k is:
`((5)/(6)) ^(3)` *
`(4)/(6)` = 500/1296;

So, the chance of rolling less than two ks is: 1125 / 1296;

So, the chance of rolling at least two ks is: 171 / 1296