Question

a) a manuscript contains 1000 pages. After proofreading, the editor found 10 typos. What is the probability that there is no more than 3 typos in a given page.

b) an urn contains 10 white balls, 15 blue balls and 25 red balls. You pick 10 balls at random from the urn. What is the probability that you will not get any red ball.

Answer 1

a.

In this question, we will use Poisson distribution with

This lambda represents the number of errors per page.

Thus, if we look at a single page, the random number of errors found in that page is Poisson distributed with parameter λ=0.01.

The probability that there is no more than 3 typos on a given page.

P(X 3)

The provided mean is λ=0.01.

We need to compute Pr(X≤3). Therefore, the following is obtained:

=

=

=0.99 + 0.0099 + 0 + 0 = 0.9999

b.

10 white balls, 15 blue balls, and 25 red balls. Total balls = 50

We picked 10 balls at random from the urn. The probability that you will not get any red ball i.e all ten balls comes from only a collection of white balls and blue balls.

P(not a single red ball)

= P(all ten balls from white and blue balls)

= P(all 10 boys from 10+15 balls)

= = 3268760/ 10272278170 = 0.0003182118