Explanation 1
Population N: Total finite items.
Loading
Loading
Lesson 14 of 18
Calculate exact success counts when sampling without replacement from a finite population.
Core lesson
Calculate exact success counts when sampling without replacement from a finite population.
Explanation 1
Population N: Total finite items.
Explanation 2
Successes K: Target items in the population.
Explanation 3
Sample n: Items drawn without replacement.
Terminology
Total finite items.
Eighty components.
Target items in the population.
Twelve defectives.
Items drawn without replacement.
Ten inspected items.
Notation and formulas
P(X=x)=C(K,x)C(N-K,n-x)/C(N,n)
Define X, its support, parameters, units, and assumptions before substituting values.
Interactive Mission
Model a finite population sampled without replacement.
P(X = x)
0.0329
F(x) = P(X <= x)
0.9945
E(X)
1.5
SD(X)
1.0629
| x | P(X=x) | Included in F(4) |
|---|---|---|
| 0 | 0.1766 | Yes |
| 1 | 0.3592 | Yes |
| 2 | 0.2963 | Yes |
| 3 | 0.1295 | Yes |
| 4 | 0.0329 | Yes |
| 5 | 0.005 | No |
| 6 | 0.0005 | No |
| 7 | 0 | No |
| 8 | 0 | No |
| 9 | 0 | No |
| 10 | 0 | No |
Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.
Worked example
Scenario
Ten items are drawn without replacement from a known lot.
Draws are dependent because the lot composition changes.
R connection
Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.
Live R Lab
Map finite-population parameters and calculate probabilities without replacement.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
Map R parameters as dhyper(x,m=K,n=N-K,k=sample_size); do not confuse both meanings of n.
Reflection
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
Assistant
Coach me through The Hypergeometric Distribution by asking about X, support, parameters, assumptions, probability notation, exact versus approximate status, and interpretation. Do not provide a quiz answer before submission or write my final capstone recommendation.
Exit check
Use conceptual hints before submitting. Full formulas, calculations, and interpretation appear afterward.
Checkpoint
Question 1 of 2. Answered 0/2. Passing score: 70%.
Resource
Explore additional discrete-distribution explanations from properly licensed or publisher resources.
DownloadResource
Download an original worksheet, formula sheet, or capstone tool for this lesson.
Download