My program is supposed to calculate the probability of a single observation (e.g. 8 successes{heads in my case}; 10 tosses/trials; probability of a head = 0.5) plus all the extreme possibilities (e.g. 9 heads out of 10 tosses; 10 heads of 10 tosses) also known as the p-value. But my professor said that the extreme is relative depending on whether or not the number of heads is greater than or equal to 1/2 * the number of trials. So I know that if there's 2 success out of 10 trials I will count down (1 head out of 10 tosses; 0 heads out of 10 tosses) when finding the probabilities to find the p-value.

I wrote the code for the program and it is running smoothly but I am not getting the correct p-value that I should be getting because for example I tested it out with success=8, trials=10 and p=0.5. I calculated by using a calculator and then testing out my program but I'm getting two different answers. I think I've made an error in my program. Can anyone look over my code to see where I've made a mistake?

CODE:

'''This program will calculate the p-value'''

import math

trials=input('Number of trials? ')
assert type(trials)==int, 'Number of trials must be an integer'
success=input('Number of successes? ')
assert type(success)==int, 'Number of successes must be an integer'
p_success=input('Probability of success? ')
assert type(p_success)==float, 'Probability of success must be a decimal number'

success_start = success
if success_start >= (0.5*trials):
    success_stop = trials + 1
    success_increment = 1
elif success_start < (0.5*trials):
    success_stop = -1
    success_increment = -1
total_prob= 0    
for n in range(success_start, success_stop, success_increment):
    combs=math.factorial(trials)/(math.factorial(success)*math.factorial(trials-success))
    prob=(p_success**success)*((1-p_success)**(trials-success))
    binom_prob=combs*prob
    total_prob=total_prob + binom_prob


print 'For', trials, 'trials and', success, 'successes, the p-value is', total_prob