In this case it's easier to calculate the probability that you're not picked the first day.
There are four essays picked the first day.
Chance of not being picked as first that day:
Not being the second of that day:
The total probability of not being picked:
So the probability of being picked:
For the first day only you could also have reasoned:
There's a chance of 4 out of 26 that I'll be picked, or
For the other days this won't work, because being picked on say the third day has to include the probabilities that you were NOT picked on the first or second day.
The first method can be extended to take this into account, in other words it is more versatile.