Conditional Probability and Independent Events

Name: Conditional Probability and Independent Events
Author: StemPy Lab

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.

3 lessons, about 1 h 15 min3 simulations10 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Conditional probability
A probability can change when you learn something new. Once you know that event $B$ has happened, the sample space shrinks to $B$ , and the probability of $A$ becomes $P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}$ . This lesson shows the reduced sample space, the formula, the notation of Indian books and of A-Level, IB and AP, and the usual slips.
1 simulation1 practice question1 Python program3 problems
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Lesson 2about 25 min
The multiplication rule and tree diagrams
Rearrange the conditional probability formula and you get the multiplication rule, $P(A \cap B) = P(A)\,P(B \mid A)$ . A tree diagram lays out the stages of an experiment: multiply along a path and add across paths. This lesson covers draws with and without replacement, chains of three events and the shortcut for "at least one".
1 simulation1 practice question1 Python program3 problems1 Python lab
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Lesson 3about 25 min
Independent events
Two events are independent when knowing that one has happened does not change the probability of the other. Then $P(A \cap B) = P(A)\,P(B)$ . This lesson tests for independence, separates it from mutually exclusive events, treats three events together and uses the idea for components in series and in parallel.
1 simulation1 practice question1 Python program4 problems1 Python lab1 question set1 note
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Conditional Probability and Independence: Practice Paper

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Conditional Probability and Independent Events

Course outline (3 lessons)