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Hint: Here, we will find the probability of the event to happen by dividing the number of favorable outcomes by the total number of outcomes.

The given digits are 0, 2, 4, 6, 8.

We have to write these digits in hundreds, tens and ones places to form three digit numbers.

Since 0 cannot occupy the hundreds place, there are only 4 ways to fill the hundreds place.

Now, there are 5 ways to fill the tens place and 5 ways to fill the ones place.

We will find the total number of 3 digit numbers is formed using the given digits.

\[4 \times 5 \times 5 = 100\]

We know that the three digit numbers formed using given digits that have the same digits are 222, 444, 666 and 888.

We will now find the probability of forming a three digit number having the same digits.

\[

\dfrac{{{\text{Number of 3 digit numbers having same digits}}}}{{{\text{Total number of 3 digit numbers using the given digits}}}} = \dfrac{4}{{100}} \\

= \dfrac{1}{{25}} \\

\]

Thus, the probability of forming a three digit number with all 3 digits being the same is \[\dfrac{1}{{25}}\].

Hence, the option D is correct.

Note: In this question, some students include 0 in the hundreds place which is wrong. Students should know the concept of probability before solving this question. Also, we are supposed to write the values properly to avoid any miscalculation.

__Complete step-by-step solution:__The given digits are 0, 2, 4, 6, 8.

We have to write these digits in hundreds, tens and ones places to form three digit numbers.

Since 0 cannot occupy the hundreds place, there are only 4 ways to fill the hundreds place.

Now, there are 5 ways to fill the tens place and 5 ways to fill the ones place.

We will find the total number of 3 digit numbers is formed using the given digits.

\[4 \times 5 \times 5 = 100\]

We know that the three digit numbers formed using given digits that have the same digits are 222, 444, 666 and 888.

We will now find the probability of forming a three digit number having the same digits.

\[

\dfrac{{{\text{Number of 3 digit numbers having same digits}}}}{{{\text{Total number of 3 digit numbers using the given digits}}}} = \dfrac{4}{{100}} \\

= \dfrac{1}{{25}} \\

\]

Thus, the probability of forming a three digit number with all 3 digits being the same is \[\dfrac{1}{{25}}\].

Hence, the option D is correct.

Note: In this question, some students include 0 in the hundreds place which is wrong. Students should know the concept of probability before solving this question. Also, we are supposed to write the values properly to avoid any miscalculation.

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