by Albert Major

Critical and Scientific Thinking

Probability and Urns

The Problem

• Initial setup involves urns with black and white balls:
  • Scenario 1: 3 black balls, 2 white balls
  • Scenario 2: 3 white balls, 2 black balls
  • Equal probability (50%) of either scenario being true

The Question

• You draw one black ball, replace it, then draw again
• What's the probability the second draw will be black?

The Solution

• For Hypothesis 1 (3 black, 2 white):
  • Probability = (3/5 × 3/5 × 0.5)
  • First 3/5: Probability of drawing black
  • Second 3/5: Probability of drawing black again
  • 0.5: Probability this hypothesis is true
• For Hypothesis 2 (2 black, 3 white):
  • Probability = (2/5 × 2/5 × 0.5)
  • Same logic applies
• Final probability: Sum of both calculations

Understanding Causation

Importance in Science

• Scientific statements often rely on causation concepts
• Examples of causal statements:
  1. Smoking → Cancer
  2. CO2 emissions → Climate change
  3. Moon's movement → Ocean tides
  4. Brain activity → Physical movement
  5. COVID-19 → 2022 inflation rates

Prediction vs. Understanding

• Key distinction: Being able to predict ≠ Understanding
• Example: Tide prediction
  • Even perfect prediction of all tides globally
  • Without understanding WHY tides occur
  • This isn't true scientific understanding
  • Need causal explanation for genuine understanding