book can be classified as either non-fiction or fiction. Suppose that \( 86 \% \) of books are classified as fiction. ) Two books are chosen at random. What is the probability that both books are fiction? b) Five books are chosen at random. What is the probability that all five books are fiction? c) What is the probability that at least one of five randomly selected books is non-fiction? Would it be unusual that at east one of five randomly selected books is non-fiction? (a) Two books are chosen at random. What is the probability that both books are fiction? The probability is 7396 . (Round to four decimal places as needed.) (b) Five books are chosen at random. What is the probability that all five books are fiction? The probability is (Round to four decimal places as needed.) (c) What is the probability that at least one of five randomly selected books is non-fiction? The probability is (Round to four decimal places as needed.) Would it be unusual that at least one of five randomly selected books is non-fiction? It would

To find the probabilities, let's start with the given information that \( 86\% \) of books are fiction, which translates to a probability of \( P(\text{Fiction}) = 0.86 \) and \( P(\text{Non-Fiction}) = 0.14 \). For part (a), the probability that both books are fiction can be calculated as: \[ P(\text{Both Fiction}) = P(\text{Fiction}) \times P(\text{Fiction}) = 0.86 \times 0.86 = 0.7396. \] For part (b), the probability that all five books are fiction is: \[ P(\text{All Five Fiction}) = P(\text{Fiction})^5 = 0.86^5 \approx 0.5132. \] (Rounding may vary slightly based on the calculator, but it should roughly be \( 0.5132 \).) For part (c), to find the probability that at least one of the five books is non-fiction, we can use the complement: \[ P(\text{At least one Non-Fiction}) = 1 - P(\text{All Fiction}) = 1 - 0.86^5 \approx 1 - 0.5132 \approx 0.4868. \] It would not be unusual for at least one of five randomly selected books to be non-fiction since it’s nearly half. Did you know that the first known library, the Library of Ashurbanipal, dates back to the 7th century BC in ancient Mesopotamia? It housed clay tablets with texts in cuneiform script, demonstrating the long-standing human desire to collect knowledge and stories! In today’s world, digital libraries and e-books allow readers to access an incredible wealth of information and literature at their fingertips. Apps and services such as Google Books, Project Gutenberg, and subscription-based platforms like Kindle Unlimited provide vast selections, showing that the classification of fiction and non-fiction continues to evolve with technology!