---
title: "Poisson: error pages in 400-page novel"
subject: "Probability and Statistics"
chapter: 2
key: "semester_5/probability_and_statistics:publisher-typo-pages-400"
source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/publisher-typo-pages-400
site: BCT Engineering
---

# Poisson: error pages in 400-page novel

Probability and Statistics · Chapter 2: Discrete Probability Distribution

- Asked in: 2073 Chaitra, 5 marks
- Video: [In a book of 450 pages, there are 400 typographical eroors. Assuming that the number of errors p...](https://www.youtube.com/watch?v=YsPFyCVjhAk) — Doubtnut
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/publisher-typo-pages-400
- Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-2

## Question

If a publisher of nontechnical books takes great pains to ensure that its books are free of typographical errors, so that the probability of any given page containing at least one such error is 0.005 and errors are independent from page to page, what is the probability that one of its 400-page novels will contain
a) Exactly one page with errors?
b) At most three pages with errors?

## Short answer

Poisson approximation with λ=np=2. P(exactly one page with errors)=0.2707; P(at most three pages)=0.8571.

## Answer

Let X = number of pages with errors in a 400-page book. n = 400 pages, p = 0.005 per page, independent, so X is binomial. Because n is large and p is small, use the Poisson approximation:

λ = np = 400 × 0.005 = 2, P(X = x) = e⁻² 2ˣ / x!, e⁻² = 0.135335.

#### a) Exactly one page with errors
P(X = 1) = e⁻² × 2 = **0.2707**

#### b) At most three pages with errors
```text
P(0) = 0.1353
P(1) = 0.2707
P(2) = 0.2707
P(3) = e⁻² · 8/6 = 0.1804
```
P(X ≤ 3) = 0.1353 + 0.2707 + 0.2707 + 0.1804 = **0.8571**

**Answer: (a) 0.2707, (b) 0.8571**

## Check yourself

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

1. Why is a Poisson approximation used for 400 pages?
   A. The pages are dependent
   B. n = 400 is large and p = 0.005 is small
   C. p is large
   D. X is continuous
   Answer: B. Large n and small p allow Poisson with lambda = np. (Key point: Approximation)

2. lambda is:
   A. p = 0.005
   B. np = 2
   C. n = 400
   D. pq = 0.005
   Answer: B. 400 x 0.005 = 2. (Key point: Lambda)

3. P(X <= 3) is:
   A. P(0)+P(1)+P(2)+P(3) = 0.8571
   B. P(3) = 0.1804
   C. 1 - P(3) = 0.8196
   D. P(0)+P(1)+P(2) = 0.6767
   Answer: A. 'At most 3' includes 0, 1, 2 and 3. (Key point: At most three)

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