QuickenBrain

Condition on information

Use natural counts to choose the right conditional denominator.

Keep only the eligible people

A survey has 20 people. Group A contains 8 Yes and 4 No responses; Group B contains 2 Yes and 6 No responses. Everyone belongs to exactly one group.

Choose uniformly from Group A. Only its 12 people are eligible, so the chance of Yes is 8/12 = 2/3. Conditioning changes the population you count.

YesNoA84B26Σ10108/12 = 2/3
The highlighted row contains all 12 eligible members of A.

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First lesson in this subject: Count equally likely outcomes

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