Question

regan 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.

	about 1 hour per week	about 3 hours per week
paperback books	6	4

what is the probability that a randomly selected club member prefers e - readers or reads about 1 hour per week?
simplify any fractions.

Explanation:

Step1: Calculate total number of members

Add all the values in the table: \(6 + 6+4 + 4=20\)

Step2: Calculate number of members who prefer e - readers or read about 1 hour per week

Use the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\)

• \(n(A)\) (e - readers): \(6 + 4 = 10\)
• \(n(B)\) (read about 1 hour): \(6+6 = 12\)
• \(n(A\cap B)\) (e - readers and read about 1 hour): \(6\)

So \(n(A\cup B)=10 + 12-6=16\)

Step3: Calculate the probability

Probability \(P=\frac{n(A\cup B)}{n(\text{total})}=\frac{16}{20}=\frac{4}{5}\)

Answer:

\(\frac{4}{5}\)