Stratified random sampling 
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*Which of the following is NOT a characteristic of stratified random sampling?


(A) Random sampling is part of the sampling procedure.
(B) The population is divided into groups of units that are similar on some characteristic.
(C) The strata are based on facts known before the sample is selected.
(D) Each individual unit in the population belongs to one and only one of the strata.
(E) Every possible subset of the population, of the desired sample size, has an equal chance of being selected.
The correct answer is (e), but why (e)? isn't every subset of the population has an equal chance of being selected. the idea of stratified sampling?
 A: The correct answer is $E$.
For stratified random sampling, we get to choose the sample size for each stratum. By picking larger/smaller numbers for one group, we're changing their probability of being selected without changing anyone else's. That means that (unless by coincidence) the chance of different samples being selected is not the same. 
It seems like you're thinking of 'simple random sampling'. That has the property of independence, which means that every possible subset of the sample size has the same chance of occurring. While simple random sampling is used in stratified random sampling, the extra leeway in picking the sample sizes for each strata changes the independence property, and means choice $E$ is not true.
A: Suppose your stratified sample is going to choose $a$ young people and $b$ old people, so a sample sized $a+b$ in total.
Then a given set sized $a+b$ made up of $a$ specific young people and $b$ specific old people has a positive probability of being sampled, while a given set of $a+b$ specific young people has no chance of being sampled.
This means it is not true that  every possible subset of the population of the desired sample size has an equal chance of being selected.
