Q: The location of trees in a park follows a Poisson distribution with rate $1$ tree per $300$ square meters. Suppose that a parachutist lands in the park at a random location. What is the probability that the nearest tree is more than $4$ meters away from where he lands?
Is this asking me to find $P(\min X_i>4)$ where $X_i$ represent the distance of tree $i$ from the parachutist?
The set of points within $4$ meters of him has area $\pi\cdot(\text{4 meters})^2.$
Thus the expected number of trees within that disk is $\dfrac{\pi\cdot 4^2}{300}\approx 0.1675516.$
That number of trees has a Poisson distribution. You're looking for the probability that that number is $0.$