Probability there is a day on Facebook without a birthday

main.rb

module Prob
  @@cache ||= {}
  def probability_of_nonbday day_of_year, number_of_friends
    return @@cache[number_of_friends][day_of_year] if
      @@cache[number_of_friends] && @@cache[number_of_friends][day_of_year]
    @@cache[number_of_friends] ||= {}
    return 0 if day_of_year < 0
    @@cache[number_of_friends][day_of_year] =
      (1-probability_of_nonbday(day_of_year-1,number_of_friends))*
      (364.to_f/365)**(number_of_friends-day_of_year) +
      probability_of_nonbday(day_of_year-1,number_of_friends)
  end
end
include Prob

announcement_triggered = false
friends_count = 0
until announcement_triggered
  if probability_of_nonbday(364,friends_count) < 0.5
    puts "At #{friends_count} friends, the probability of having a day without"+
         "birthdays is #{probability_of_nonbday(364,friends_count)}"
    announcement_triggered = true
  end
  friends_count += 1
end

# At 2482 friends, the probability of having a day withoutbirthdays is 0.49960360037037066