Bernaullis Trial

If we do the question question in the video by expectation method the result is N/2.

Here is what i did, Let’s say the expected number of students selecting a single digit number is x, probability of single digit is 9/100.

Therefore, x=x*(9/100) + (N-x)*(91/100).
solving this we get, x=N/2.
I know this solution does not matches with solution given.
May i know what mistake did i make?

hello @subhamjaiswal885

why u r adding this term?
this way u r only calculating the mean