Examples: Binomial distribution as applied to the 100-year flood https://tonyladson.wordpress.com/2015/06/22/100-year-flood-binomial-distribution/

OneHundredYearBin.R

dbinom(0,100,0.01) # zero 1% floods in 100 years
dbinom(1,100,0.01) # one 1% floods in 100 years
dbinom(2,100,0.01) # two 1% floods in 100 years
dbinom(3,100,0.01) # three 1% floods in 100 years
dbinom(4,100,0.01) # four 1% floods in 100 years
dbinom(5,100,0.01) # five 1% floods in 100 years

# at least 1 1% flood in 100 years
1 - pbinom(0,100, 0.01) 

# Sample calculation
# Exactly 2 1% floods in 100 years
choose(100,2) * 0.01^2 * (1 - 0.01)^98
#[1] 0.1848648


par(oma = c(1, 2, 0, 0))
barplot(dbinom(0:5,100,0.01),
        ylim = c(0, 0.4),
        las = 1, 
        names.arg = 0:5,
        ylab = 'Probability',
        xlab = 'Number of 100-year floods in 100 years')

set.seed(2000)
rbinom(10, 100, 0.01)
#[1] 0 1 0 1 2 1 3 1 2 1
# number of 100-year floods in each of 10 100-year sequences