Probability · Combined events & tree diagrams
Chapter 1 · 3
The idea
Conditional probability
Why "given that" shrinks the sample space to the group you were told about, so the denominator becomes that group's total — and why P(A given B) and P(B given A) are two different questions with two different answers.
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Probability · Combined events & tree diagrams
Conditional probability
Why "given that" shrinks the sample space to the group you were told about, so the denominator becomes that group's total — and why P(A given B) and P(B given A) are two different questions with two different answers.
Why it works
"Given that" shrinks the sample space
Every probability you have met so far has the same shape: favourable outcomes over the sample space — everything that could have happened. A "given that" question does not change how you count the top of the fraction. It changes the bottom, because the words given that tell you a whole chunk of the sample space did not happen and is no longer in the running. The idea in one sentence: "given that" shrinks the sample space to the group you were told about.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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