Juana is surveying a town to determine whether residents prefer fiction or nonfiction books based on whether they solve crossword puzzles in their free time. She collected her data and organized it into a two-way table.

Question asked: "Do you prefer fiction or nonfiction books?"

[tex]
\[
\begin{tabular}{|c|c|c|c|}
\hline
& \begin{tabular}{c} Solves \\ Crossword \\ Puzzles \end{tabular} & \begin{tabular}{c} Does not \\ Solve \\ Crossword \\ Puzzles \end{tabular} & Total \\
\hline
Fiction & 70 & 280 & 350 \\
\hline
Nonfiction & 131 & 519 & 650 \\
\hline
Total & 201 & 799 & 1000 \\
\hline
\end{tabular}
\]
[/tex]

Juana has been learning about independence, so she's wondering if solving crossword puzzles and fiction/nonfiction preference are independent. Answer the following questions. Round to 4 decimal places if needed.

1. [tex] P(\text{fiction} \mid \text{Solves Crossword Puzzles}) = \square [/tex]

2. [tex] P(\text{fiction} \mid \text{Does not solve Crossword Puzzles}) = \square [/tex]

3. [tex] P(\text{fiction}) = \square [/tex]

Answer :

1 P(fiction | Solves Crossword Puzzles) ≈ 0.3483

2 P(fiction | Does not solve Crossword Puzzles) ≈ 0.3504

3 P(fiction) = 0.3500

1 Calculating P(fiction | Solves Crossword Puzzles):

P(fiction and solves crossword puzzles) = 70

P(solves crossword puzzles) = 201

So, P(fiction | Solves Crossword Puzzles) = 70 / 201

≈ 0.3483.

2 Calculating P(fiction | Does not solve Crossword Puzzles):

P(fiction and does not solve crossword puzzles) = 280

P(does not solve crossword puzzles) = 799

So, P(fiction | Does not solve Crossword Puzzles) = 280 / 799

≈ 0.3504.

3 Calculating P(fiction):

P(fiction) = Total who prefer fiction / Total surveyed = 350 / 1000

= 0.3500.