Label batches before consulting the random-number table, so their labels are independent of the test results. A uniformly random permutation of , restricted to a smaller label set, induces a uniformly random ordering of that set. This provides a simple rejection-and-restriction scheme:
- For A, label each day's six batches . Use a fresh permutation, discard labels , and test the first remaining batch. Repeat independently on each working day. Each daily batch has inclusion probability , and five batches are tested per week.
- For B, label the fifteen weekly morning batches . Discard label 16 from a fresh permutation and choose the first three remaining labels. Use an independent permutation for the afternoon stratum. Every three-element subset within a stratum is equally likely, and each batch has inclusion probability . Six batches are tested per week.
- For C, label the weekdays . Keep the first label in this range from a fresh permutation and test all six batches on that day. Repeat independently each week. Every day, and hence every batch, has inclusion probability ; six batches are tested per week.
With independent random digits instead, rejection sampling gives the same uniform choices: for A keep only digits ; for C keep only . For B, use uniform two-digit numbers, retain labels , and reject repeats within a three-batch sample. Taking residues modulo six or fifteen from a table whose range is not divisible by that number would give unequal probabilities. These are respectively day-stratified simple random sampling, morning/afternoon stratified sampling, and a one-day design using cluster sampling. The printed word “rest” for A is interpreted as “test”, consistently with the surveillance task. If it instead meant leaving one batch untested, choose that omitted batch uniformly and test the other five; this alternative would test 25 batches per week, with inclusion probability , and has a different testing budget.
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