Mathematics, Statistics & Data Science
High School (11–12)
Statistics and Probability › Conditional Probability and Bayes' TheoremStatistics and Probability › Random Variables and Probability DistributionsChapter 16Conditional Probability and Distributions
A friend peeks at your card and says it is a heart. Your chances change at once. A test says a patient is ill, and still the patient is probably healthy. Both surprises come from the same idea: new information changes a probability. This chapter shows how to update a probability with conditional probability, how to chain events with tree diagrams, how to turn a result around with Bayes' theorem, and how to describe a repeated trial with a random variable and the binomial distribution. It covers the unit of the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP. Python checks every probability in exact fractions.
Part of Mathematics · High School (11–12) (chapter 16)
Following adds this path to your dashboard and enrolls you in the 3 courses you can open, so you can start right away.
Courses in This Path (3)
1.Not started2.
Conditional Probability and Independent Events
You roll a die behind a screen, and a friend peeks and says the number is even. What is the chance it is a six? The answer is no longer one in six. Learn to shrink the sample space with a condition, to multiply along the branches of a tree diagram, and to decide when two events do not affect each other at all. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
Total Probability and Bayes' Theorem
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.