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Statistics for Everyday Life · Module 3

Probability and Prediction

Module 1 taught you to describe data; Module 2 taught you to judge evidence. This module turns to the hardest and most useful part of statistics: reasoning about what happens next when you cannot know for sure.

You will learn to think in probabilities rather than certainties, to update beliefs with conditional probability and base rates, to read the shape of a distribution, to weigh choices with expected value, to see through streaks and regression to the mean, to understand what forecasts can and cannot promise, and to put probability to work in real decisions.

Lessons
7 lessons
Estimated time
~6-8 hours
Assessment
Module quiz included

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Lessons

Lesson 1 · 16 min

Thinking in Probabilities

Lesson 2 · 16 min

Conditional Probability and Base Rates

Lesson 3 · 16 min

Probability Distributions

Lesson 4 · 16 min

Expected Value and Decisions

Lesson 5 · 16 min

Randomness, Streaks, and Regression

Lesson 6 · 16 min

Forecasting and Prediction

Lesson 7 · 17 min

Probability in Practice

Check your understanding

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Probability and Prediction — Module Assessment

14 questions · pass mark 75%

  1. 1.You have made 50 forecasts you each marked '80% confident.' Which outcome shows you were well calibrated?
  2. 2.A colleague says a one-off product launch has a '75% chance' of succeeding. Which reading of probability is this?
  3. 3.A test is 99% accurate and a condition affects 1 in 1,000 people. You test positive. Roughly what is the chance you have the condition?
  4. 4.In the Monty Hall problem, after the host reveals a goat, why should you switch doors?
  5. 5.What does a probability distribution give you that a single average does not?
  6. 6.Why can assuming a normal distribution be dangerous for something like financial losses?
  7. 7.How is the expected value of an uncertain choice calculated?
  8. 8.Why can a bet with positive expected value still be a bad decision?
  9. 9.A roulette wheel lands on black eight times running. Why is red not more likely on the next spin?
  10. 10.Flight instructors found that cadets praised after a great manoeuvre usually did worse next time, and cadets criticized after a poor one usually improved. What best explains this?
  11. 11.A forecaster says "70% chance of rain" and the day stays dry. What does this tell us about the forecast?
  12. 12.According to Tetlock's forecasting research, what most distinguishes the best forecasters?
  13. 13.A screening test for a condition affecting 1 in 100 people catches 90% of real cases but gives a false positive for 9% of healthy people. You test positive. Roughly how likely are you to actually have the condition?
  14. 14.A wager has a slightly positive expected value but requires staking everything each round, with a real chance of losing almost all your savings. Why might it still be a bad decision?
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