Suppose that S is a subset of m units from U, and suppose S has mh units from stratum h, for h = 1, . . . , H. Let Zi = 1 if unit i is selected to be in the final sample and 0 otherwise; similarly, let Fi = 1 if unit i is selected to be in the stratified sample and 0 otherwise, and let Di = 1 if unit i is selected to be in the subsample chosen from the stratified sample and 0 otherwise. Then the probability that S is chosen to be the sample is

We can write P (S) as

Then,

Also

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P(S) = P(Zi = 1, İ E S. and Zi = 0, i S) P(F, = 1, i E S) Nm1 I m1 nH n2 m2 Ni TLI NH nH n2 total number of stratified samples containing S number of possible stratified samples n1 MH 7AV TLH RH m1 mm2 Note that for each h, mh nh mh rmh Tlh (Nhmh)! nh Consequently th Ilh mh so this procedure results in an SRS of size m