Data Science — Probability

Basic probability

# P(A) = favorable outcomes / total outcomes
def probability(favorable, total):
    return favorable / total

# Probability of rolling 6
p_six = probability(1, 6)
print(f"P(6) = {p_six:.4f}")

Conditional probability

# P(A|B) = P(A and B) / P(B)
def conditional_prob(p_a_and_b, p_b):
    return p_a_and_b / p_b

# Bayes' theorem
def bayes(p_b_given_a, p_a, p_b):
    return (p_b_given_a * p_a) / p_b

Common distributions

from scipy import stats

# Normal
normal = stats.norm(0, 1)
print(f"PDF at 0: {normal.pdf(0)}")

# Binomial
binom = stats.binom(n=10, p=0.5)
print(f"P(X=5): {binom.pmf(5)}")

# Poisson
poisson = stats.poisson(mu=3)
print(f"P(X=2): {poisson.pmf(2)}")

Expected value

def expected_value(values, probabilities):
    return sum(v * p for v, p in zip(values, probabilities))

values = [1, 2, 3, 4, 5]
probs = [0.1, 0.2, 0.3, 0.2, 0.2]
print(f"E[X] = {expected_value(values, probs)}")

Mini Practice

1. Calculate basic probabilities
2. Apply Bayes' theorem
3. Work with distributions
4. Compute expected values

Up Next

Continue with Hypothesis Testing - Statistical tests.