--- title: "Poisson: typist mistakes per page" subject: "Probability and Statistics" chapter: 2 key: "semester_5/probability_and_statistics:typist-mistakes-poisson" source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/typist-mistakes-poisson site: BCT Engineering --- # Poisson: typist mistakes per page Probability and Statistics · Chapter 2: Discrete Probability Distribution - Asked in: 2075 Chaitra, 5 marks - Video: [Assuming that the typing mistakes per page committed by a typist follows a Poisson distribution, fi](https://www.youtube.com/watch?v=TyAaKN8IydU) — B MATHS ZONE | Kishan Sir - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/typist-mistakes-poisson - Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-2 ## Question A typist made 2.6 mistakes per page on average, find the probability that the page typed by him, i) there is no mistake ii) at least two mistakes iii) at most 3 mistakes. ## Short answer Using Poisson distribution with mean 2.6, probability of no mistake is 0.0743, at least two mistakes is 0.7326, and at most three mistakes is 0.7360. ## Answer Mistakes per page are rare, independent events over a page, so X ~ **Poisson** with mean λ = 2.6: P(X = x) = e⁻²·⁶ (2.6)ˣ / x!, with e⁻²·⁶ = 0.074274. ```text x P(X = x) 0 0.074274 1 0.074274 × 2.6 = 0.193111 2 0.193111 × 2.6/2 = 0.251045 3 0.251045 × 2.6/3 = 0.217572 ``` #### i) No mistake P(X = 0) = **0.0743** #### ii) At least two mistakes P(X ≥ 2) = 1 − P(0) − P(1) = 1 − 0.0743 − 0.1931 = **0.7326** #### iii) At most three mistakes P(X ≤ 3) = 0.0743 + 0.1931 + 0.2510 + 0.2176 = **0.7360** **Answer: (i) 0.0743, (ii) 0.7326, (iii) 0.7360** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why Poisson? A. Mistakes per page are random events with a mean rate lambda = 2.6 B. Waiting for r successes C. Fixed number of trials D. Finite lot Answer: A. Counts of rare random events per unit. (Key point: Poisson) 2. P(X=0)? A. 0.1931 B. 2.6 C. 0.0743 D. 0.2510 Answer: C. e^-2.6 = 0.0743. (Key point: No mistake) 3. How is P(X>=2) found? A. 1 - P(0) - P(1) = 0.7326 B. P(2) only C. P(0)+P(1) D. 1 - P(2) Answer: A. 1 - 0.0743 - 0.1931. (Key point: At least two) 4. P(X<=3)? A. 0.2176 B. 0.7326 C. 0.5 D. 0.7360 Answer: D. Sum of P(0) to P(3) = 0.7360. (Key point: At most three) ## Related in Probability and Statistics - [Poisson: error pages in 400-page novel](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Apublisher-typo-pages-400) — Probability and Statistics, chapter 2 - [Poisson process; intersection accidents](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Apoisson-process-accidents-intersection) — Probability and Statistics, chapter 2 - [Poisson: accidents among 1000 taxi drivers](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Ataxi-accidents-poisson-1000) — Probability and Statistics, chapter 2 - [Independent events; computer errors per week](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Aindependent-events-computer-errors) — Probability and Statistics, chapter 1, asked 2× - [Two companies: wages and combined SD](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Atwo-companies-wage-combined-sd) — Probability and Statistics, chapter 1 - [Binomial: defective lenses in packet](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Alenses-defective-packet-of-10) — Probability and Statistics, chapter 2 ## Related in other subjects - [Nepal least responsible but most affected](https://www.bctengineer.com/question.md?key=semester_7%2Ftechnology_environment_and_society%3Anepal-least-responsible-cc) — Technology, Environment and Society, chapter 6 - [Poisson call arrival probabilities](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Apoisson-call-arrivals) — Telecommunications, chapter 6 - [Poisson arrival probabilities in 15 minutes](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Apoisson-arrivals-probability-15-minute) — Transportation Engineering II, chapter 1 - [Main geohazards versus man-made hazards](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Amain-geohazards-manmade) — Engineering Geology II, chapter 5, asked 2×