Question
Charlotte joined a book club to spend more quality time with her 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 11 4
About 3 hours per week 5 12
About 5 hours per week 6 6
What is the probability that a randomly selected club member prefers paperback books and does not read about 1 hour per week?
Simplify any fractions.
E-readers Paperback books
About 1 hour per week 11 4
About 3 hours per week 5 12
About 5 hours per week 6 6
What is the probability that a randomly selected club member prefers paperback books and does not read about 1 hour per week?
Simplify any fractions.
Answers
Answered by
GPT-4o mini
To find the probability that a randomly selected club member prefers paperback books and does not read about 1 hour per week, we first need to determine the total number of club members and then find the number of club members that fit the criteria of preferring paperback books and reading more than 1 hour per week.
**Step 1: Total number of club members**
We will sum the values in each category:
- E-readers:
- About 1 hour: 11
- About 3 hours: 5
- About 5 hours: 6
- Paperback books:
- About 1 hour: 4
- About 3 hours: 12
- About 5 hours: 6
Calculating the total for each preference:
- Total for E-readers = 11 + 5 + 6 = 22
- Total for Paperback books = 4 + 12 + 6 = 22
So, the total number of club members is:
\[
22 (E-readers) + 22 (Paperback) = 44
\]
**Step 2: Count club members who prefer paperback books and do not read about 1 hour per week**
Paperbacks:
- About 1 hour: 4 members
- About 3 hours: 12 members
- About 5 hours: 6 members
To find the number of members who prefer paperback books and do not read about 1 hour per week:
\[
\text{Total paperback books} = 4 \text{ (about 1 hour)} + 12 \text{ (about 3 hours)} + 6 \text{ (about 5 hours)} = 22
\]
\[
\text{Members who prefer paperback books and read more than 1 hour} = 12 (about 3 hours) + 6 (about 5 hours) = 18
\]
**Step 3: Calculate the probability**
The probability \( P \) that a randomly selected club member prefers paperback books and does not read about 1 hour per week is given by
\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{18}{44}
\]
**Step 4: Simplify the fraction**
To simplify \( \frac{18}{44} \), we find the greatest common divisor (GCD) of 18 and 44, which is 2:
\[
\frac{18 \div 2}{44 \div 2} = \frac{9}{22}
\]
Thus, the final simplified probability that a randomly selected club member prefers paperback books and does not read about 1 hour per week is
\[
\boxed{\frac{9}{22}}
\]
**Step 1: Total number of club members**
We will sum the values in each category:
- E-readers:
- About 1 hour: 11
- About 3 hours: 5
- About 5 hours: 6
- Paperback books:
- About 1 hour: 4
- About 3 hours: 12
- About 5 hours: 6
Calculating the total for each preference:
- Total for E-readers = 11 + 5 + 6 = 22
- Total for Paperback books = 4 + 12 + 6 = 22
So, the total number of club members is:
\[
22 (E-readers) + 22 (Paperback) = 44
\]
**Step 2: Count club members who prefer paperback books and do not read about 1 hour per week**
Paperbacks:
- About 1 hour: 4 members
- About 3 hours: 12 members
- About 5 hours: 6 members
To find the number of members who prefer paperback books and do not read about 1 hour per week:
\[
\text{Total paperback books} = 4 \text{ (about 1 hour)} + 12 \text{ (about 3 hours)} + 6 \text{ (about 5 hours)} = 22
\]
\[
\text{Members who prefer paperback books and read more than 1 hour} = 12 (about 3 hours) + 6 (about 5 hours) = 18
\]
**Step 3: Calculate the probability**
The probability \( P \) that a randomly selected club member prefers paperback books and does not read about 1 hour per week is given by
\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{18}{44}
\]
**Step 4: Simplify the fraction**
To simplify \( \frac{18}{44} \), we find the greatest common divisor (GCD) of 18 and 44, which is 2:
\[
\frac{18 \div 2}{44 \div 2} = \frac{9}{22}
\]
Thus, the final simplified probability that a randomly selected club member prefers paperback books and does not read about 1 hour per week is
\[
\boxed{\frac{9}{22}}
\]