Question

What is the probability of selection for any man in a proportionate random sample, where a sample of 100 will be drawn from a population of 1,000 that is 50% male and 50% female?

Answer 1

Working Principle: Stratified Random Sampling

nx = (Nx/N)*n

where:
nx = sample size for stratum x
Nx = population size for stratum x
N = total population size
n = total sample size

Given:

Nx = 100
N = 1000
n = 0.5*(1000) = 500

Required: Probability of Man to be selected

Solution:

nx = (Nx/N)*n
nx = (100/1000)*500 = 50 men

ny = (Nx/N)*n
ny = (100/1000)*500 = 50 women


Probability of Man to be selected = nx/(nx + ny)*100 = 50/(50+50)*100 = 50%

ANSWER: 50%