alleryStart learning →Sampling without replacement makes successive picks dependent because:
AThe population grows each time
BThe sample space stays fixed
CEvery outcome becomes equally likely
DEarlier picks change later probabilities
Answer & Solution
Correct answer: D. Earlier picks change later probabilities
1. Removing a member changes what remains available to be drawn.
2. In sampling without replacement, the probabilities for the second pick are affected by the result of the first pick.
3. That dependence is exactly what independence rules out.
4. Sampling with replacement leaves the pool unchanged between picks, so the draws stay independent.
5. The population shrinks rather than grows, which rules out the second option.
_Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 3 'Probability Topics', sections 3.1-3.5_
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