vos Savant binomial calcs

binomial_calcs.r

# Libraries
require("ggplot2")

# Define variables
n = 4
p = .25
k = c(1:4)
# Calculate binomial probabilities for X=[1:4]
probs <- dbinom(x=k, size=n, prob=p)

# Probability of being selected at least once, P(X >= 1)
sum(probs)

# Plot P(X=k) vs. K
qplot(k, probs, geom="point") +
    xlab("k, # of times picked per year") +
    ylab("P(X=k)")


# Probability of not being selected, P(X = 0)
## Binomial calculation
dbinom(x=0, size=n, prob=p)
## Probability approximation
(1-p)^n