Disjoint Is Not the Far Side of Independent. It Is the Far Side of the Line

You'll learnwhat mutually exclusive means in a sample space, why the addition rule subtracts the overlap exactly once, and why two events with positive probability can be disjoint or independent but never both.

Hold two events at 0.50 and 0.40 and let the overlap between them move. Every legal version of the pair is one value of that overlap, and two of them have names. At an overlap of 0 the events are mutually exclusive and knowing B happened drops P(A) from 0.50 to zero. At an overlap of 0.20 — which is 0.50 × 0.40 — they are independent and knowing B happened changes nothing at all. Those are different points on the same line, and the second is the only one where the word "unrelated" applies. The arithmetic half is smaller and just as heavily tested: the overlap you subtract in an "or" question is exactly the overlap disjoint events do not have, and a survey that adds 70% to 55% and reports 1.25 has counted the students who do both of them twice. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · DISJOINT EVENTS · THE ADDITION RULE · CONDITIONAL PROBABILITY · v2

Disjoint at overlap 0, independent at 0.20, and never both at once

Before you start

What you're looking at

Fifty-two cards as a grid, and later two events drawn as bars on one lane, where a width is a probability and the width they share is their overlap.

The question

Mutually exclusive and independent are both ways of saying two events are separate. Where does each one actually sit?

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