Overview
On this page, we discuss the concept of independence of events in a sample space.
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Understand the intuitive idea of independent events and the precise formulation of the notion using conditional probability.
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
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Use the simplified form of the intersection law when the two events involved are known to be independent.
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Understand that for a collection of three or more events, each pair of events can be pairwise independent and despite this, the collection as a whole may not be independent.
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Understand that events being mutually exclusive or independent are two different concepts.
To prepare for class
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Watch the first half (up to 11:17) of the following video (by jbstatistics) which introduces the independence of two events:
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Watch the following video (by Brendan Cordy) which shows a few simple examples.
After class
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Watch the second half of the first video above (by jbstatistics), paying special attention to the explanations at 18:17 (that we can sometimes assume independence due to the nature of the situation) and at 19:25 (that the word “independent” in every-day language can often mean something else).
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Watch the following video (again by jbstatistics) which discusses whether two mutually exclusive events can be independent:
