Calculate Probabilities (pmf)

import scipy.stats as stats # import library

# full formula: stats.binom.pmf(x, n, p)
# binom stands for binomial distribution, pmf stands for probability mass function

# value of interest
x = 3

# sample size/no. of trials
n = 10

# calculate probability
prob_1 = stats.binom.pmf(x, n, 0.5) # last parameter represents probability of success (p)
print(prob_1)

# To calculate probability over a range
# for observing between 4 to 6 heads from 10 coin flips - add them together
prob_1 = stats.binom.pmf(4, 10, 0.5) + stats.binom.pmf(5, 10, 0.5) + stats.binom.pmf(6, 10, 0.5)
print(prob_1)

# for observing more than 2 heads from 10 coin flips (ie. from 3 to 10)
# use the 1 minus the sum of some values as a shortcut for unwanted 0 to 2 heads
prob_2 = 1 - (stats.binom.pmf(0, 10, 0.5) + stats.binom.pmf(1, 10, 0.5) + stats.binom.pmf(2, 10, 0.5))
print(prob_2)