laalaguer/possibility.py

## possibility.py
# Python3

# In 100 numbers,
# Exactly has (n) numbers, that are <= value
# The possibility.
def f(n, value):
  a = 1 - value/100
  b = value/100

  # Numbers that are > 8
  part_1 = a ** (100 - n)  # (0.92) ^ (100-n)

  # Numbers that are <=8
  part_2 = b ** n # (0.08) ^ n

  # Pick up (n) slots, to accommodate those (n) numbers.
  # part_3 = C(100, n) = (100 !) / ((100 - n)! * n!) = (1 * 2 * ... * 100) / ((1 * 2 * ... *(100-n) * (1 * 2 * ... n))
  part_3 = 1

  for i in range(1, 100+1):
    part_3 = part_3 * i

  for i in range(1, (100-n) + 1):
    part_3 = part_3 / i

  for i in range(1, n + 1):
    part_3 = part_3 / i

  return part_1 * part_2 * part_3

# In 100 numbers,
# Have x numbers, that are <= y,
# The possibly.
def test(x, y):
  total = 0
  for i in range(x, 100+1): # [x,...100]
    total += f(i, y)
  print('at least have '+ str(x) + ' and more numbers, that are <=' + str(y), ',', str(round(total * 100)) + '%' )


for i in range(8, 20 + 1):
  test(5, i)
  test(6, i)
  test(7, i)
  test(8, i)
  test(9, i)
  test(10, i)

  print()
	# Python3

	# In 100 numbers,
	# Exactly has (n) numbers, that are <= value
	# The possibility.
	def f(n, value):
	a = 1 - value/100
	b = value/100

	# Numbers that are > 8
	part_1 = a ** (100 - n) # (0.92) ^ (100-n)

	# Numbers that are <=8
	part_2 = b ** n # (0.08) ^ n

	# Pick up (n) slots, to accommodate those (n) numbers.
	# part_3 = C(100, n) = (100 !) / ((100 - n)! * n!) = (1 * 2 * ... * 100) / ((1 * 2 * ... (100-n) (1 * 2 * ... n))
	part_3 = 1

	for i in range(1, 100+1):
	part_3 = part_3 * i

	for i in range(1, (100-n) + 1):
	part_3 = part_3 / i

	for i in range(1, n + 1):
	part_3 = part_3 / i

	return part_1 * part_2 * part_3

	# In 100 numbers,
	# Have x numbers, that are <= y,
	# The possibly.
	def test(x, y):
	total = 0
	for i in range(x, 100+1): # [x,...100]
	total += f(i, y)
	print('at least have '+ str(x) + ' and more numbers, that are <=' + str(y), ',', str(round(total * 100)) + '%' )


	for i in range(8, 20 + 1):
	test(5, i)
	test(6, i)
	test(7, i)
	test(8, i)
	test(9, i)
	test(10, i)

	print()