---
title: "Poker test, 1000 four-digit numbers (2069)"
subject: "Simulation and Modeling"
chapter: 6
key: "semester_8/simulation_and_modeling:poker-test-numerical-2069-bhadra"
source: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/poker-test-numerical-2069-bhadra
site: BCT Engineering
---

# Poker test, 1000 four-digit numbers (2069)

Simulation and Modeling · Chapter 6: Random Number

- Asked in: 2069 Bhadra (old course), 8 marks
- Video: [Poker Test (4 digits) | Random Number Independency | Simulation & Modelling | in Nepali](https://www.youtube.com/watch?v=BNIt43dxQaY) — Monkey D. Luffy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/poker-test-numerical-2069-bhadra
- Whole chapter: https://www.bctengineer.com/md/semester_8/simulation_and_modeling/chapter-6

## Question

A sequence of 1000 four digit numbers has been generated and analysis indicates the following combinations with frequencies:

| Combination (i) | Observed Frequency (Oi) |
|---|---|
| Four different digits | 570 |
| One pair | 380 |
| Two pairs | 34 |
| Three like digits | 15 |
| Four like digits | 1 |
|  | 1000 |

Based on poker test check whether the numbers are independent. Use α=0.10 and N=4 is 7.78

## Short answer

Chi-square test statistic = 28.97. Critical value χ²0.10,4 = 7.78. Since 28.97 > 7.78, H0 (independence) is rejected at α=0.10; the numbers are not independent.

## Answer

**Setup.** H0: the numbers are independent. H1: they are not. N = 1000, five classes, df = 4, α = 0.10, χ²0.10,4 = 7.78.

Probabilities for four-digit numbers: 0.504, 0.432, 0.027, 0.036, 0.001. Ei = 1000 × probability.

| Pattern | Probability | Oi | Ei | (Oi − Ei)²/Ei |
|---|---|---|---|---|
| Four different | 0.504 | 570 | 504 | 8.643 |
| One pair | 0.432 | 380 | 432 | 6.259 |
| Two pairs | 0.027 | 34 | 27 | 1.815 |
| Three of a kind | 0.036 | 15 | 36 | 12.250 |
| Four of a kind | 0.001 | 1 | 1 | 0.000 |

**χ0² = 28.97**

**Conclusion.** Since 28.97 > 7.78, H0 is **rejected** at α = 0.10; the numbers are not independent. The largest contributions are "three like digits" (15 observed against 36 expected, 12.25) and "four different digits" (570 against 504, 8.64).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. At alpha = 0.10 with df = 4, which critical value is used?
   A. 9.488
   B. 7.78
   C. 11.07
   D. 5.99
   Answer: B. chi-square 0.10,4 = 7.78 as given. (Key point: Critical value)

2. Three like digits: observed 15, expected 36. Contribution?
   A. 12.25
   B. 21
   C. 0.58
   D. 441
   Answer: A. (15 - 36)^2 / 36 = 441/36 = 12.25. (Key point: Three-like contribution)

3. Four different: observed 570, expected 504. Contribution?
   A. 66
   B. 8.64
   C. 0.13
   D. 4356
   Answer: B. 66^2 / 504 = 4356/504 = 8.64. (Key point: Four different contribution)

4. chi-square0 = 28.97 vs 7.78 means:
   A. Independent
   B. Not independent (reject H0)
   C. Random and uniform
   D. Need alpha = 0.05
   Answer: B. 28.97 > 7.78, so independence is rejected at alpha = 0.10. (Key point: Decision)

## Close variants set in other exams

- [Poker test, 1000 four-digit numbers (2070 Magh)](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Apoker-test-numerical-2070-magh) — Simulation and Modeling, chapter 6, asked 3×
- [Poker test, 10,000 five-digit numbers (2072)](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Apoker-test-numerical-2072-ashwin) — Simulation and Modeling, chapter 6, asked 4×

## Related in Simulation and Modeling

- [Poker test, 1000 four-digit numbers (2072 Magh)](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Apoker-test-numerical-2072-magh) — Simulation and Modeling, chapter 6
- [Poker test, 1000 four-digit numbers (2073)](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Apoker-test-numerical-2073-magh) — Simulation and Modeling, chapter 6
- [Poker test, 10,000 five-digit numbers (2074)](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Apoker-test-numerical-2074-magh) — Simulation and Modeling, chapter 6, asked 2×
- [Poker test, 10,000 four-digit values (2070)](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Apoker-test-numerical-2070-bhadra) — Simulation and Modeling, chapter 6