To determine the probability that a randomly selected club member prefers paperback books and does not read about 1 hour per week, we'll start by analyzing the given data and following a step-by-step approach.
1. Identify the Total Number of Members:
From the given table, we categorize the members based on their reading preferences and weekly reading hours.
- E-readers, About 1 hour per week: 11 members
- Paperback books, About 1 hour per week: 4 members
- E-readers, About 3 hours per week: 5 members
- Paperback books, About 3 hours per week: 12 members
- E-readers, About 5 hours per week: 6 members
- Paperback books, About 5 hours per week: 6 members
To find the total number of club members:
[tex]\[
\text{Total members} = 11 + 4 + 5 + 12 + 6 + 6 = 44 \text{ members}
\][/tex]
2. Determine the Number of Members Who Prefer Paperback Books and Do Not Read About 1 Hour per Week:
We are interested in members who prefer paperback books and read for about 3 hours or 5 hours per week.
- Paperback books, About 3 hours per week: 12 members
- Paperback books, About 5 hours per week: 6 members
Therefore, the total number of members who prefer paperback books and do not read about 1 hour per week is:
[tex]\[
\text{Prefer paperback and not 1 hour} = 12 + 6 = 18 \text{ members}
\][/tex]
3. Calculate the Probability:
The probability [tex]\( P \)[/tex] of selecting a club member who prefers paperback books and does not read about 1 hour per week is given by the ratio of the number of favorable outcomes to the total number of club members:
[tex]\[
P = \frac{\text{Prefer paperback and not 1 hour}}{\text{Total members}} = \frac{18}{44}
\][/tex]
4. Simplify the Fraction:
The fraction [tex]\(\frac{18}{44}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
[tex]\[
\frac{18 \div 2}{44 \div 2} = \frac{9}{22}
\][/tex]
Thus, the simplified probability that a randomly selected club member prefers paperback books and does not read about 1 hour per week is:
[tex]\[
\boxed{\frac{9}{22}}
\][/tex]
In decimal form, this probability is approximately [tex]\(0.409\)[/tex].
