Given that we are Rolling a four-sided dice and We need to find what is the probability of rolling a 4 three times out of four?

As we are rolling a four sides dice four times => Number of cases = \(4^4\)

To get 4 three times out of 4 let's find out those three places out of 4 where 4 will come. This can be done in 4C3 ways
=> \(\frac{4!}{3!*1!}\) = 4 ways

Now, those 3 4's can occupy those places in 1 way each (As there is only one 4 out of 4)

The fourth roll can take any value except 4 => 3 ways (1, 2, 3)

=> Total ways = 4 * 1 * 1 * 1 * 3 = 12 ways

=> Probability of rolling a 4 three times out of four = \(\frac{12}{4^4}\) = \(\frac{3}{64}\)

So, Answer will be E
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems