Probabilities, mean, and variance

General
#1

Hypothetical case: This is a farm that I divided into 10 regions, and I put that the probability of finding a species of cows in this area is 0.3.

n <-10 #number of regions
p <- 0.3#probability of success in each trial

How can I calculate and plot the density function and find the mean and variance of the random variable?

In terms of probabilities, is it possible to find 6 or more regions with the cows? How I can do it or with what function?

#2

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)

#4

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#3

well, assuming that they are cows in a farm