Question

applying the conditional probability formula

a book shelf holds twenty books. eleven are hard-covered, nine of the books are nonfiction, and four of the nonfiction books are hard-covered, as shown in the venn diagram. let event h be a hard-covered book and let event n be a nonfiction book.

a book is chosen randomly. complete the steps to find the probability that the book is nonfiction given that it is hard-covered.

1. find the probability that a chosen book is nonfiction and hard-covered. \\(p(n \cap h) = \\)
2. find the probability that a chosen book is hard-covered. \\(p(h) = \\)
3. calculate the conditional probability. \\(\frac{p(n \cap h)}{p(h)} = \\)

Explanation:

Find the intersection probability

Using the Union and Intersection of Events knowledge point

$$ P(N \cap H) = \frac{4}{20} = \frac{1}{5} $$

Find the probability of the condition

Using the Union and Intersection of Events knowledge point

$$ P(H) = \frac{7 + 4}{20} = \frac{11}{20} $$

Calculate the conditional probability

Using the Conditional Probability knowledge point

$$ P(N | H) = \frac{P(N \cap H)}{P(H)} = \frac{\frac{4}{20}}{\frac{11}{20}} = \frac{4}{11} $$

Answer:

Question 1

Find the probability that a chosen book is nonfiction and hard-covered. \(P(N \cap H) =\) <blank>\(\frac{4}{20}\)</blank>

Question 2

Find the probability that a chosen book is hard-covered. \(P(H) =\) <blank>\(\frac{11}{20}\)</blank>

Question 3

Calculate the conditional probability. \(\frac{P(N \cap H)}{P(H)} =\) <blank>\(\frac{4}{11}\)</blank>