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satt comments on How do I make sample size matter? - Less Wrong Discussion
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The likelihood distribution is a mathematical restatement of the earlier sentence "The fraction of defective items produced is this: for the first machine, 5%; for the second machine, 3%; for the third machine, 1%". In other words, a (uniformly) randomly chosen item produced by the first machine has a 5% chance of being defective, so P(B|A1) = 0.05, et mutatis mutandis for the other two machines.
The sample size comes in at "If an item is chosen at random from the total output and is found to be defective" — "an item", hence N = 1.
This information is encoded in the likelihood, but that's not explicitly noted so it may not be obvious. Had more than one item been chosen at random from the output, the likelihood would be different (and the hypothesis being tested, "what is the probability that it was produced by the third machine?", would have to be changed too to make sense with the new N).