The problem: 

Out of 20 exam tickets, 16 tickets are "good". Tickets are carefully mixed, and students take turns pulling one ticket. Who has the better chance to draw a "good" ticket the first or the second student in the queue?

My attempt: 

Obviously the probability of the first student getting a "good" ticket is $16/20 = 4/5 = 0.8$

Now here's where I'm confused. I considered two cases. If the first student got a "good" ticket then the chances of the second student are $15/19 = 0.789$, so lower than the first student. 

However if the first student didn't get a "good" ticket, the chances of the second student are $16/19 =0.842$, so slightly better chances than the first one. 

So is the answer "depends on whether the first student gets a "good" ticket"?