Probability Lab 🎲

Coin tosso, Bayes ka theorem samjho, binomial distribution dekho — sab visual aur interactive!

🪙 Lab 1: Large Numbers ka Law — Frequency → Probability

Coin toss karo baar baar. Dekho: jaise trials badhte hain, frequency (observed) theoretical probability (0.5) ke paas aati jaati hai! Yahi Law of Large Numbers hai.

🔵🔴 Lab 2: Bayes Theorem — Colored Balls Visual

Bag 1 mein R red + B1 blue balls, Bag 2 mein R2 red + B2 blue balls. Ek ball red aayi — kis bag se aayi hogi? Yahi Bayes ka sawaal hai!

4 6 3 2

📊 Lab 3: Binomial Distribution — Bar Chart

n trials, har trial mein success probability p. P(X=k) = ⁿCₖ·pᵏ·(1-p)ⁿ⁻ᵏ. n aur p change karo — distribution ka shape badle dekho!

10 0.50

🌳 Lab 4: Total Probability — Tree Diagram

Ek machine defective part banati hai. Tree dekho — P(defective) kaise calculate hoti hai? Har path ki probability multiply karo, phir add karo!

0.60 0.05 0.10