count.rb

arr = (0...20).to_a

p0 = 0
(0..8).each do |x|
  p0 += 0.475 ** x * 0.525 ** (20 - x) * arr.combination(x).count
end

p1 = 0.475 ** 9 * 0.525 ** 11 * arr.combination(9).count

p2 = 0
(10..20).each do |x|
  p2 += 0.475 ** x * 0.525 ** (20 - x) * arr.combination(x).count
end

puts "p0 = #{p0}"
puts "p1 = #{p1}"
puts "p2 = #{p2}"

puts "sum = #{p0 + p1 + p2}"