A book contains

    \[\mathbf{85}\]

pages. A page is chosen at random. What is the probability that the sum of the digits on the page is

    \[\mathbf{8}\]

?
A book contains

    \[\mathbf{85}\]

pages. A page is chosen at random. What is the probability that the sum of the digits on the page is

    \[\mathbf{8}\]

?

Solution:

We know that,

Number of pages in the book

    \[=\text{ }85\]

Number of possible outcomes

    \[=\text{ }n\left( S \right)\text{ }=\text{ }85\]

Out of

    \[85\]

pages, pages that sum up to

    \[8\text{ }=\text{ }\left\{ 8,\text{ }17,\text{ }26,\text{ }35,\text{ }44,\text{ }53,\text{ }62,\text{ }71,\text{ }80 \right\}\]

So, pages that sum up to

    \[8\text{ }=\text{ }n\left( E \right)\text{ }=\text{ }9\]

Hence, probability of choosing a page with the sum of digits on the page equals

    \[8\text{ }=\text{ }n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }9/85\]