probability

probs

expected.x <- function(d, a, h) {
  sum(sapply(0:h, function(y) prob.justy(d, a, h, y)) * 0:h)
}
prob.xormore <- function(d, a, h, x) {
  if (d >= h && min(a, h) >= x)
    sum(prob.justy.nocheck(d, a, h, x:min(a, h)))
  else {
    0
  }
}
prob.justy <- function(d, a, h, y) {
  if (d >= h)
    prob.justy.nocheck(d, a, h, y)
  else
    0
}
prob.justy.nocheck <- function(d, a, h, y) {
  choose(a, y) * choose(d-a, h-y) / choose(d, h)
}