A bookshelf contains 4 mystery novels, 6 science fiction novels, and 5 biography books. If… — ACT

A bookshelf contains $4$ mystery novels, $6$ science fiction novels, and $5$ biography books. If one book is chosen at random from the bookshelf, what is the probability that the chosen book is NOT a science fiction novel?

$\frac{3}{5}$ Answer
B
$\frac{2}{5}$
C
$\frac{2}{3}$
D
$\frac{3}{2}$
E
$\frac{11}{15}$

Answer

The probability that the chosen book is NOT a science fiction novel is

\frac{3}{5}

The correct answer is

\frac{3}{5}

. To find the probability of selecting a book that is not science fiction, divide the number of books that are not science fiction (

4

mystery +

5

biography =

9

) by the total number of books (

4 + 6 + 5 = 15

). This yields

\frac{9}{15}

, which simplifies to

\frac{3}{5}

Step-by-Step Solution

Find the total number of books on the shelf

Total books =

4 + 6 + 5 = 15

The sample space consists of all mystery, science fiction, and biography books combined.

Count the number of books that are NOT science fiction

Non-science fiction books =

4 + 5 = 9

The mystery novels (

4

) and biography books (

5

) are the favorable outcomes.

Calculate the probability and simplify the fraction

Probability =

\frac{9}{15} = \frac{3}{5}

Probability is the number of favorable outcomes divided by the total number of outcomes.

Key Concept

Basic Probability of Complementary Events

Estimated Time:45s

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