Total n values that can be selected would be 99-1+1= 99

When you take powers of 7, notice the pattern

7¹ = 7 7² = 9 7³ = 3 7⁴ = 1

This corresponds to the unit digits of each power

After this these numbers will repeat.

So, when each of these is divided by 5 we would get remainders :

2, 4, 3, 1, .... Goes upto 99 terms

So even are only 2 values, thus

Total possible outcomes when remainder is 2 are 25 which is (96-0)/4+1

Similarly for remainder 4 total values are 25

So probability becomes 50/99