Question

Gavin joined a book club to spend more quality time with his cousin. At the first meeting, club members recorded how many hours a week they typically read and whether they preferred e-readers or paperback books. E-readers Paperback books About 1 hour per week 6 5 About 3 hours per week 4 5 What is the probability that a randomly selected club member prefers paperback books given that the club member reads about 1 hour per week? Simplify any fractions.

Answer 1

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,

`P(\frac{\text{paperback}}{1\text{ hr per week}})`

Apply Bayes' Theorem,

`\begin{gathered} P(\frac{\text{paperback}}{1\text{ hr per week}})=\frac{P(\text{paperback})* P(\frac{1\text{ hr per week}}{\text{paperback}})}{P(\text{paperback})* P(\frac{1\text{ hr per week}}{\text{paperback}})+P(\text{e-book})* P(\frac{1\text{ hr per week}}{\text{e-book}})} \\ P(\frac{\text{paperback}}{1\text{ hr per week}})=((10)/(20)*(5)/(10))/(((10)/(20)*(5)/(10))+((10)/(20)*(6)/(10))) \\ P(\frac{\text{paperback}}{1\text{ hr per week}})=(5)/(5+6) \\ P(\frac{\text{paperback}}{1\text{ hr per week}})=(5)/(11) \end{gathered}`

Thus, the required probability is 5/11.