Question

A library has $3000$ books of fiction and $4000$ books of non-fiction. What is the probability that a book selected at random is non-fiction?

Answer 1

Step Finding the probability of the book being non-fiction:

The event is selecting a book at random and it being non-fiction.

There are $3000$ books of fiction in the library.

There are $4000$ books of non-fiction in the library.

So, the number of favorable outcomes of selecting a non fiction book is $4000$.

The total number of outcomes will be the number of books the library has.

$3000+4000=7000$

So, the total number of outcomes is $7000$.

The formula for probability is

$Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}$

$$\begin{gathered} \Rightarrow P(non-fiction)=\frac{4000}{7000} \\ \therefore P(non-fiction)=\frac{4}{7} \end{gathered}$$

Therefore, the probability of a book being non-fiction is $\frac{4}{7}$.