It is asked to determine the probability that a randomly selected club member prefers paperback books given that the club member reads about 1 hour per week. This can be mathematically represented as,
[tex]P(\frac{\text{paperback}}{1\text{ hr per week}})[/tex]Apply Bayes' Theorem,
[tex]\begin{gathered} P(\frac{\text{paperback}}{1\text{ hr per week}})=\frac{P(\text{paperback})\times P(\frac{1\text{ hr per week}}{\text{paperback}})}{P(\text{paperback})\times P(\frac{1\text{ hr per week}}{\text{paperback}})+P(\text{e-book})\times P(\frac{1\text{ hr per week}}{\text{e-book}})} \\ P(\frac{\text{paperback}}{1\text{ hr per week}})=\frac{\frac{10}{20}\times\frac{5}{10}}{(\frac{10}{20}\times\frac{5}{10})+(\frac{10}{20}\times\frac{6}{10})} \\ P(\frac{\text{paperback}}{1\text{ hr per week}})=\frac{5}{5+6} \\ P(\frac{\text{paperback}}{1\text{ hr per week}})=\frac{5}{11} \end{gathered}[/tex]Thus, the required probability is 5/11.
