#! /usr/bin/env python
"""
 cointoss.py is program which calculates the binomial coefficient via
 a user defined function(from pascal.py).  The program calculates the
 probability a coin tossed n times comes up heads k times 

The probability P(k out of n) = binomial (n k)/2**n 

Results for n =137 & k = 63
 The probility of getting 63 heads by flipping 137 coins is: 0.0438723882434
 The probility of getting 63 or more heads in 137 coin flips is: 0.847378610933

 Paul Eugenio 
 PHZ4151C
 Jan 27, 2019
"""

# program header code
from __future__ import division, print_function
#from math import factorial

def factorial( n ):
    if n == 1:
        return n
    else:
        return n*factorial(n-1)


def binomial(n, k):
    """  Binomial coefficient   (n k) = n!/(k!(n-k)! """
    return ( factorial(n) // (factorial(k)*factorial(n-k)) )

#
# main
#


#
# Probility = (n k)/2**2

# For n=137 & k=53, the exact probility is 0.002
# whereas the probility of 53 or more times is  0.997
# Also, the probility of 0 or more times heads come up is 1 as it should.
# 

# initialize variables
n = int(raw_input("Enter the total number of coin tosses: "))
k = int(raw_input("Enter the number of times that heads comes up: "))


print("\n")
print("The probility of getting", k, "heads by flipping", n,"coins is:",
      binomial(n,k)/2**n )

probility = 0
for i in range(k, n+1):
	probility += binomial(n,i) / 2**n


print("The probility of getting", k, "or more heads in", n,
      "coin flips is:", probility)