Total Probability and Bayes' Theorem

Name: Total Probability and Bayes' Theorem
Author: StemPy Lab

A factory has three machines, and one faulty bolt is found in the box. Which machine made it? You know how often each machine makes a faulty bolt, and now you want to run the question backwards. Split the world into cases, add the cases with the law of total probability, and reverse a condition with Bayes' theorem. Then meet the traps that catch even careful readers, from screening tests to the game show with three doors. It covers the second part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.

3 lessons, about 1 h 25 min3 simulations10 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
The law of total probability
When the world splits into cases that cannot overlap and that cover every possibility, the probability of an event is a sum over the cases. Multiply the chance of each case by the chance of the event in that case, then add. This lesson shows the partition, the law of total probability, the tree diagram that adds the right paths and the usual slips.
1 simulation1 practice question1 Python program3 problems
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Lesson 2about 30 min
Bayes' theorem
Bayes' theorem turns a probability around. You know how likely a result is under each possible cause. The theorem tells you how likely each cause is once you have seen the result. This lesson gives the formula, the words prior, likelihood and posterior, and the method of natural frequencies, with factories, urns and a medical test.
1 simulation1 practice question1 Python program4 problems1 Python lab
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Lesson 3about 30 min
Screening tests and other traps
A good test can still give a poor answer. This lesson names the four numbers that describe a test, shows why the rate of an illness matters so much, and meets the traps that catch careful readers: the prosecutor's fallacy, the two-child puzzle, the game with three doors and the updating of a result by a second test.
1 simulation1 practice question1 Python program3 problems1 Python lab1 question set1 note
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Total Probability and Bayes' Theorem: Timed Test

10 questions · 25 min

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Total Probability and Bayes' Theorem

Course outline (3 lessons)

The law of total probability

Bayes' theorem

Screening tests and other traps

Test Your Learning

Your teacher

Discussion (0)