Suppose a population has 26 members identified with the letters A through Z.
a) You select one individual at random from this population. What is the probability of selecting individual A?
b) Assume person A gets selected on an initial draw, you replace person A into the sampling frame, and then take a second random draw. What is the probability of drawing person A on the second draw?
c) Assume person A gets selected on the initial draw and you sample again without replacement. What is the probability of drawing person G on the second draw?
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a) The probability of selecting individual A on the first draw is 1/26 since there are 26 members in the population.
b) Since person A is replaced back into the sampling frame, the probability of drawing person A on the second draw is still 1/26. Each draw is independent of the previous one.
c) If person A is selected on the initial draw and not replaced into the sampling frame, then the probability of drawing person G on the second draw would be 1/25. This is because after person A is selected and removed from the population, there are now only 25 members left in the sampling frame.
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