---
title: "Poker test, 1000 four-digit numbers (2070 Magh)"
subject: "Simulation and Modeling"
chapter: 6
key: "semester_8/simulation_and_modeling:poker-test-numerical-2070-magh"
source: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/poker-test-numerical-2070-magh
site: BCT Engineering
---

# Poker test, 1000 four-digit numbers (2070 Magh)

Simulation and Modeling · Chapter 6: Random Number

- Asked in: 2070 Magh, 7 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-2070-magh
- 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 and frequencies:

| Combination (i) | Observed Frequency (Oi) |
|---|---|
| Four different digits | 540 |
| One pair | 380 |
| Two pairs | 54 |
| Three like digits | 25 |
| Four like digits | 1 |
|  | 1000 |

Based on poker test check whether the numbers are independent. Use α=0.05 and χ² = 9.49

## Short answer

The chi‑square statistic is 39.19, with 4 degrees of freedom and critical value 9.49 at α=0.05. Since 39.19 > 9.49, the hypothesis of independence is rejected.

## Answer

**Setup.** H0: the numbers are independent. H1: they are not. N = 1000, five classes, df = 4, α = 0.05, χ²0.05,4 = 9.49.

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 | 540 | 504 | 2.571 |
| One pair | 0.432 | 380 | 432 | 6.259 |
| Two pairs | 0.027 | 54 | 27 | 27.000 |
| Three of a kind | 0.036 | 25 | 36 | 3.361 |
| Four of a kind | 0.001 | 1 | 1 | 0.000 |

**χ0² = 39.19**

**Conclusion.** Since 39.19 > 9.49, H0 is **rejected**; the numbers are not independent. The biggest contribution is from "two pairs" (54 against 27 expected, contribution 27.0).

## Check yourself

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

1. For N = 1000, what is the expected number of 'one pair'?
   A. 432
   B. 504
   C. 27
   D. 380
   Answer: A. 1000 x 0.432 = 432. (Key point: Expected frequency)

2. Two pairs: observed 54, expected 27. Contribution?
   A. 27.0
   B. 2.0
   C. 54.0
   D. 13.5
   Answer: A. (54 - 27)^2 / 27 = 729/27 = 27. (Key point: Two pairs contribution)

3. What is df for the five pattern classes?
   A. 5
   B. 3
   C. 4
   D. 1000
   Answer: C. df = 5 - 1 = 4, with critical 9.49. (Key point: Degrees of freedom)

4. chi-square0 = 39.19 vs 9.49 means:
   A. Accept independence
   B. Reject independence
   C. Accept uniformity
   D. Increase alpha
   Answer: B. 39.19 > 9.49, so H0 is rejected. (Key point: Decision)

## Close variants set in other exams

- [Poker test, 1000 four-digit numbers (2069)](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Apoker-test-numerical-2069-bhadra) — 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