A certain publishing company surveyed readers of three books it publishes (Books A, B, and C). In the diagram, each...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

• The largest single group among respondents (38%) is those who read all three books.
• Book B is the most-read and central: everyone who read both A and C also read B, evidenced by the zero in the 'A and C only' region.
• Over 60% of Book A readers read all three books \(\mathrm{(0.38/0.58 ≈ 0.655)}\), confirming the high overlap among A readers.
• The probability a randomly selected respondent read only A and C is zero, since the 'A and C only' region is empty.

Step-by-Step Solution

Question 1: Conditional Probability of Reading All Three Books Among Readers of a Specific Book

Complete Statement:

Among the respondents who had read [BLANK], the probability that one selected at random had read all three books is greater than 0.60.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: Among the respondents who had read [BLANK]
    • Meaning: We are considering only those people who read a particular book.
    • Relation to Chart: We look at the total percentage next to each book in the Venn diagram.
    • Important Implications: This sets the 'given that' condition for a conditional probability calculation.

• Statement Breakdown 2:
  • Key Phrase: probability that one selected at random had read all three books
    • Meaning: Out of those who read the chosen book, what fraction also read all three books?
    • Relation to Chart: This is the proportion at the intersection of all three circles — the middle of the Venn diagram.
    • Important Implications: We're looking for \(\mathrm{P(all\ three\ |\ specific\ book) = P(all\ three) ÷ P(that\ book)}\).

• What is needed: Which single book, when chosen as the [BLANK], gives \(\mathrm{P(all\ three\ |\ that\ book) \gt 0.60}\).

Solution:

• Condensed Solution Implementation:
  Compute the conditional probability for each book: \(\mathrm{P(all\ three\ |\ A)}\), \(\mathrm{P(all\ three\ |\ B)}\), and \(\mathrm{P(all\ three\ |\ C)}\). Choose the book with a result above 0.60.
• Necessary Data points:
  \(\mathrm{P(all\ three\ books) = 0.38}\); \(\mathrm{P(Book\ A) = 0.58}\); \(\mathrm{P(Book\ B) = 0.81}\); \(\mathrm{P(Book\ C) = 0.72}\).
  • Calculations Estimations:
    \(\mathrm{P(all\ three\ |\ A) = 0.38 ÷ 0.58 ≈ 0.655}\); \(\mathrm{P(all\ three\ |\ B) = 0.38 ÷ 0.81 ≈ 0.469}\); \(\mathrm{P(all\ three\ |\ C) = 0.38 ÷ 0.72 ≈ 0.528}\).
  • Comparison to Answer Choices:
    Only Book A has \(\mathrm{P \gt 0.60}\) (about 0.655).

FINAL ANSWER Blank 1: Book A

Question 2: Probability That a Random Survey Respondent Read Only Books A and C

Complete Statement:

The probability that a randomly selected respondent had read only Books A and C is [BLANK].

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: randomly selected respondent
    • Meaning: We are considering the entire survey population.
    • Relation to Chart: Use the Venn diagram's proportions directly.

• Statement Breakdown 2:
  • Key Phrase: had read only Books A and C
    • Meaning: These respondents read both A and C but NOT Book B.
    • Relation to Chart: This refers to the A∩C region of the diagram outside B's circle.

• What is needed: The proportion represented by just the overlap of A and C (excluding B).

Solution:

• Condensed Solution Implementation:
  Read the value in the Venn diagram representing 'only A and C.'
• Necessary Data points:
  From the diagram, the region representing 'only A and C' is labeled as 0.00.
  • Calculations Estimations:
    No calculation is required: the diagram shows this value is 0.00.
  • Comparison to Answer Choices:
    0.00 is an option, and matches exactly.

FINAL ANSWER Blank 2: 0.00

Summary

For Blank 1, only Book A satisfies the condition that more than 60% of its readers read all three books, since \(\mathrm{0.38/0.58 ≈ 0.655}\). For Blank 2, the probability a randomly chosen respondent read only A and C is 0.00, directly given by the Venn diagram. So, the answers are: Book A and 0.00.

Question Independence Analysis

The two questions are independent. The first requires a conditional probability calculation about all three books among readers of a specific book, while the second only requires direct reading of a single region in the Venn diagram. The answer to one does not affect the solution to the other.