Assuming that the probability of success in any one region is independent of the probability of success in any other region (i.e., the gators don't congregate) for number of regions observed is

n <- 10 #number of regions
p <- 0.3 #probability of success in each trial
for (i in 1:n) print(p^i)
#> [1] 0.3
#> [1] 0.09
#> [1] 0.027
#> [1] 0.0081
#> [1] 0.00243
#> [1] 0.000729
#> [1] 0.0002187
#> [1] 6.561e-05
#> [1] 1.9683e-05
#> [1] 5.9049e-06

^{Created on 2020-11-15 by the reprex package (v0.3.0.9001)}