🔩 Probability Concepts – With Visual Examples

👥 Sample vs. Population (Visual)

Population: All items we care about. Sample: The subset we actually inspect.

Population (e.g., 10,000 bolts) Sample (200 bolts)

The sample is the small part of the population that we measure.

📊 Sample Space and Events (Visual)

Sample Space (S): All possible outcomes. Event: A set of outcomes we care about.

Sample Space S A B

Example: S = {good, defective}; A = {defective}.

🧪 What Is a Random Experiment?

A random experiment is a process whose result can vary even when repeated the same way.

🎲 What Is Probability?

Probability measures how likely an event is. It’s between 0 (never) and 1 (always).

📦 Summary

📝 In Class Exercise (ICE): Apply What You Learned (ICE)

Instructions: Choose one scenario below. Answer in 4–6 sentences. Use the words sample, population, event, sample space, and probability correctly.

  1. 🔌 Online Test and Power Outage:
    80 students are taking an online exam. You learn that 3 students lost power during the test. If you randomly select one student, define the sample space and the event of “losing power.” Is this a random experiment? What is the probability the chosen student lost power?
  2. 🔧 Bolt Inspection:
    A factory produces 10,000 bolts daily. A sample of 100 bolts is tested, and 5 are defective. What are the population, sample, and event? Estimate the probability a bolt is defective. How is this helpful in quality control?
  3. 🏥 COVID Test Results:
    At a clinic, 8% of people test positive for COVID. What is the sample space of this experiment? Define an event using that space. What is the probability someone tests positive? Is this situation a random experiment?