A metal detector misses 1% of the time

What is the probability that the first person missed is among the fist 50 persons scanned ?

I saw this as we want 1 success in 50 trials so p=1 we apply $\displaystyle p (1-p)^ {49} $

After some thought I think I spotted my mistake. The negative binomial is x trialsuntila success so applying it to this situation means that the 50th person is missed.

The solution is P(X < or equal to 50) = $\displaystyle 1 - 0.99^{50}$

Can some one help me clearly distinguish between then negative binomial and this situation but explaining the logic behind the solution ?