Which case is true for hyper geometric distribution________________?
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Answer: D. Both (b) & (c) but not (a)
Explanation
Hypergeometric distributions model sampling without replacement from a finite population containing two groups. Removing items without replacement changes the population composition, causing success probabilities to change between trials. Consequently, successive trials are statistically dependent, confirming both statements in option D are correct. Sampling without replacement alters the remaining pool of items, directly affecting subsequent probability calculations. Dependent trials mean the outcome of a previous draw influences the probability of success on the next draw. Jakob Bernoulli and subsequent mathematicians formalized these dependent sampling distribution models.
Quality assurance inspectors use hypergeometric models when pulling multiple items simultaneously from production batches. Card game probabilities rely on dependent successive draws where available cards decrease in the deck. Genetics researchers use hypergeometric models to analyze allele sampling without replacement in populations. Option A is incorrect because probability does not remain constant when sampling occurs without replacement. Option B is only partially correct because trial dependence is also a defining feature of the process. Option C is only partially correct because changing success probabilities is equally integral to the process.
- Subject
- Mathematics
- Category
- Statistics
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- —
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- medium
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