Question

a book is to be randomly chosen from the library. the probability that a randomly - chosen book is fiction is $\frac{1}{3}$. the probability that a randomly - chosen book has a white cover is $\frac{1}{4}$. the probability that a randomly - chosen book is fiction and has a white cover is $\frac{1}{24}$. what is the probability that a randomly - chosen book from the library is fiction or has a white cover? a $\frac{5}{8}$ b $\frac{13}{24}$ c $\frac{1}{24}$ d $\frac{1}{8}$

Explanation:

Step1: Recall probability formula

We use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, where $A$ is the event of choosing a fiction - book and $B$ is the event of choosing a book with a white cover.

Step2: Identify given probabilities

Let $P(A)=\frac{1}{3}$, $P(B)=\frac{1}{4}$, and $P(A\cap B)=\frac{1}{24}$.

Step3: Substitute values into formula

$P(A\cup B)=\frac{1}{3}+\frac{1}{4}-\frac{1}{24}$.
First, find a common denominator, which is 24. Then $\frac{1}{3}=\frac{8}{24}$ and $\frac{1}{4}=\frac{6}{24}$.
So $P(A\cup B)=\frac{8}{24}+\frac{6}{24}-\frac{1}{24}=\frac{8 + 6-1}{24}=\frac{13}{24}$.

Answer:

B. $\frac{13}{24}$