Urn Marble Transfer

Problem 3.7 • Transfer a marble then draw - conditional probability

🏺 Urn Experiment

1. Initial State
2. Transfer
3. Draw from B
Urn A
→
Transfer
Urn B

📊 Probability Analysis

P(Red from B) = 0.500
P(Blue from B) = 0.500
Law of Total Probability:
P(Red from B) = P(Red|Transfer Red)·P(Transfer Red) + P(Red|Transfer Blue)·P(Transfer Blue)

⚙️ Urn Contents

Urn A (Source)

Red Marbles3
Blue Marbles2

Urn B (Destination)

Red Marbles4
Blue Marbles3

📐 Calculation Breakdown

P(Transfer Red) = 3/5
P(Transfer Blue) = 2/5

If Red transferred:
P(Red from B) = 5/8

If Blue transferred:
P(Red from B) = 4/8