Use two valid extreme arrangements to separate what is guaranteed from what is merely possible.
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First lesson in this subject: Count equally likely outcomes
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There are 20 tiles. Twelve have marking A and thirteen have marking B. A tile may have both markings, one marking or neither. Every tile is equally likely to be drawn.
Adding 12 and 13 gives 25, but there are only 20 tiles. At least 5 must have been counted twice. These 5 or more tiles have both markings. The two markings have not been described as independent.
You are reading the opening. Members read every lesson and guide in full. A free account reads the first lesson in each subject in full.
You are reading the opening. Your free account reads the first lesson in each subject in full. Members read every lesson and guide in full.
First lesson in this subject: Count equally likely outcomes
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Practice · Use incomplete counts to decide what must, might or cannot be true about chance.
Book · Count outcomes, update chances with new information, and compare decisions through worked examples.
Previous lesson · Build the distribution of sums before choosing a counter to an opponent.
Next lesson · Separate independent components from routes that share a bottleneck, then compare two upgrades.
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