Exploring a model of team availability. You must assemble a group of N people from a team of T people, each of which is available with a certain probability.

team_availability.py

from pylab import *
from scipy.misc import comb

def diff_simp(p):
    return 7*3*(p**5)*(1-p)**2 + 7*(p**6)*(1-p) + p**7 - p**3


# the probability of a assembling [n] of [t] people, each being available with
# probability [p]
def availability(p,n,t):
    return sum([comb(t,ni)*p**ni*(1-p)**(t-ni) for ni in range(n,t+1)])

# generalized difference, n1/t1 vs. n2/t2 people
def diff(p, n1, t1, n2, t2):
    p1 = availability(p,n1,t1)
    p2 = availability(p,n2,t2)
    return p1 - p2

xs = linspace(0,1,100)
ys = [diff_simp(i) for i in xs]
ys2 = [diff(i,5,7,3,3) for i in xs] # for different configurations,
                                    # change 5/7 3/3

plot(xs,ys)
plot(xs,ys2) # note these plots are the same
title('Diff in Prob between assembling a team of 5/7 people and 3/3 people')
xlabel('Probability of availability')
ylabel('Difference in Probabilities')
show()