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🕵️ Conditional Probability

Conditional probability is answering the question: "How does my guess change if I learn a new clue?"

☁️ The Rain Example​

  • What is the probability it rains today? Maybe 20%.
  • Now, what is the probability it rains today, GIVEN that you see dark clouds outside? Now it jumps to 80%.

The notation for "Probability of Rain GIVEN Clouds" is: P(Rain∣Clouds)P(\text{Rain} | \text{Clouds}).

🐍 Python Implementation​

Let's calculate conditional probability from a dataset!

import pandas as pd

# 1 = Yes, 0 = No
data = {
    'Saw_Clouds': [1, 1, 0, 1, 0, 0, 1, 0],
    'Rained':     [1, 1, 0, 0, 0, 0, 1, 0]
}
df = pd.DataFrame(data)

# P(Rain) -> total rain days / total days
p_rain = df['Rained'].mean()

# P(Rain | Clouds) -> Only look at days where Saw_Clouds == 1
cloudy_days = df[df['Saw_Clouds'] == 1]
p_rain_given_clouds = cloudy_days['Rained'].mean()

print(f"P(Rain) = {p_rain * 100}%")
print(f"P(Rain | Clouds) = {p_rain_given_clouds * 100}%")