## Binomial probability function 
plot(0:40, dbinom(0:40, 40, 0.5),
     type = "h",
     xlab = "Number of A preferences",
     ylab = "Probability")

## Highlighting the observations leading to a discrepancy
## of 8 or more preferences
x <- c(0:12, 28:40)
segments(x, rep(0, length(x)),
         x, dbinom(x, 40, 0.5),
         lwd = 4)
}