Question

At a used-book sale, adult books and children’s books are sold. Of the adult books, 70 are nonfiction and 30 are fiction. Of the children’s books, 60 are nonfiction and 100 are fiction. If a book is selected at random,

(a) Find the probability that the book is a children’s book.

(b) Find the probability that the book is nonfiction.

Answer 1

a) 0.6154

b) 0.5

Explanation:

We are given the following in the question:

Adult books:

Number of non-fiction = 70

Number of fiction = 30

Total number of adult books =

= Number of non-fiction + Number of fiction

`=70+30\\=100`

Children books:

Number of non-fiction = 60

Number of fiction = 100

Total number of Children books =

= Number f non-fiction + Number of fiction

`=60+100\\=160`

Total number of books =

= Number of adult books + Number of Children book

`=100 +160\\=260`

Formula:

`\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}`

a) probability that the book is a children’s book.

`\text{P(Children book)} = \frac{\text{Number of children book}}{\text{Total number of books}}\\\\\text{P(Children book)} = (160)/(260) = 0.6154`

b) probability that the book is nonfiction.

`\text{P(Non-fiction)} = \frac{\text{Number of Non-fiction book}}{\text{Total number of books}}\\\\\text{P(Non-fiction)} = (70+60)/(260) = 0.5`