A book can be classified as either non-fiction or fiction. Suppose that \( 86 \% \) of books are classified as fiction. (a) 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 least 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 .4182 . (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 .5818 . (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 not be unusual that at least one of five randomly selected books is non-fiction.

(a) The probability that both books are fiction is given by the formula: \[ P(\text{both fiction}) = P(\text{first book is fiction}) \times P(\text{second book is fiction}) \] Given that \( 86\% \) of books are classified as fiction, the probability of a book being fiction is \( 0.86 \). Therefore, the probability that both books are fiction is: \[ P(\text{both fiction}) = 0.86 \times 0.86 = 0.7396 \] (b) The probability that all five books are fiction is given by the formula: \[ P(\text{all fiction}) = P(\text{first book is fiction}) \times P(\text{second book is fiction}) \times P(\text{third book is fiction}) \times P(\text{fourth book is fiction}) \times P(\text{fifth book is fiction}) \] Using the same probability of a book being fiction as in part (a), the probability that all five books are fiction is: \[ P(\text{all fiction}) = 0.86 \times 0.86 \times 0.86 \times 0.86 \times 0.86 = 0.4182 \] (c) The probability that at least one of five randomly selected books is non-fiction is given by the formula: \[ P(\text{at least one non-fiction}) = 1 - P(\text{all fiction}) \] Using the probability of all five books being fiction from part (b), the probability that at least one of five randomly selected books is non-fiction is: \[ P(\text{at least one non-fiction}) = 1 - 0.4182 = 0.5818 \] It would not be unusual that at least one of five randomly selected books is non-fiction.