http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_Binomial_Distributions

# Exercise 1:
# To graph a binomial distribution in R 
# First we can calculate all probabilities
# X is binomial(10,0.5)
x <- seq(0,10)
px <- dbinom(x,  size = 10, prob = 0.5)
barplot(px, space = 0, xlab = "X", ylab = "P(X)", ylim = c(0, .25),
        main = "Binomial probability distribution", names.arg =x)

#a. X is b(10,0.5) , find P(X = 3), E(X), sd(X)
dbinom(3, 10, 0.5)
ex <- sum(x*px)
sdx <- sqrt(sum(x ^ 2 * px) - ex ^ 2)

#b. X is b(10,0.1) , find P(1 <= X <= 3)
sum(dbinom(1:3, 10, 0.1))
#or
pbinom(3, 10, 0.1) - pbinom(0, 10, 0.1)

#c. X is b(10,0.9) , find P(5 < X < 8), P(X < 8), P(X <= 7), P(X >= 9) 
pbinom(7, 10, 0.9) - pbinom(5, 10, 0.9)
pbinom(7, 10, 0.9)
pbinom(7, 10, 0.9)
pbinom(8, 10, 0.9, lower.tail = FALSE)


#d. X is b(30,0.1) , find P(X > 2)

pbinom(1, 30, 0.1, lower.tail = FALSE)
#or
1 - pbinom(1, 30, 0.1)


#Exercise 5:
par1 <- par()
par(bg = "KHAKI")
x <- seq(0, 10)
px <- dhyper(x, 13, 39, 10)
barplot(px, space = 0, xlab = "X", ylab = "P(X)", ylim = c(0, .35), 
        main = "Hypergeometric probability distribution", col.main = "blue",
        names.arg =x, cex.names = .8, las = 2, col = "skyblue")


#Exercise 6: P(X = 5)
dhyper(5, 13, 39, 10)
#Exercise 7 and 8: 
x <- seq(0, 10)
px <- dhyper(x, 50, 950, 10)
barplot(px, space = 0, xlab = "X", ylab = "P(X)",  
        main = "Hypergeometric probability distribution", col.main = "blue",
        names.arg =x, cex.names = .8, las = 2)

dhyper(2, 50, 950, 10)
dbinom(2, 10, 0.05)
#Exercise 9
x <- seq(0, 20)
px <- dhyper(x, 40, 10, 20)
barplot(px, space = 0, xlab = "X", ylab = "P(X)", ylim = c(0, .3), 
        main = "Hypergeometric probability distribution \n and Binomial approximation", col.main = "blue",
        names.arg =x, cex.names = .8, las = 2, col = "skyblue")
py <- dbinom(x, 20, 0.8)
barplot(py, space = 0, xlab = "X", ylab = "P(X)",  
           add = TRUE, col = "transparent", yaxt = "n", border = "red")

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http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_More_Examples
#Example 2
#a. 
phyper(0, 10, 990, 50, lower.tail = FALSE)
phyper(0, 5, 495, 25, lower.tail = FALSE)

#b. 
phyper(1, 10, 990, 50, lower.tail = FALSE)
phyper(1, 5, 495, 25, lower.tail = FALSE)

#c.
phyper(1, 100, 900, 50, lower.tail = FALSE)
phyper(1, 50, 450, 25, lower.tail = FALSE)



#Example 3:
pbinom(309, 567, .58, lower.tail = FALSE)