A certain publishing company surveyed readers of three books it publi

Question

t2.PNG A certain publishing company surveyed readers of three books it publishes (Books A, B, and C). In the diagram, each circle represents one of these books. Next to the label for each circle is the proportion of the total number of survey respondents who had read the corresponding book. Each number in the diagram shows the proportion of the total number of respondents who had read the book(s) represented by the circle or circles in which it appears. For example, the proportion of the number of respondents who had read Book C was 0.72, and the proportion who had read Books B and C but not Book A was 0.20. Select from each drop-down menu the option that completes the statement so that it most accurately reflects the information provided. Among the repondents who had read GRAPH_1_PLACEHOLDER , the probability that one selected at random had read all three books is greater than 0.60. The probability that a randomly selected respondent had read only Books A and C is GRAPH_2_PLACEHOLDER .

chetan2u · Accepted Answer

Among the respondents who had read Book ?, the probability that one selected at random had read all three books is greater than 0.60. 
0.38 have read all three books, so 0.38 > X * 0.60 or X <  \frac{0.38}{60}  or X<63.3
 Only Book A has total number of respondents who read it less than 63. Hence ? = Book A

The probability that a randomly selected respondent had read only Books A and C is 
Straight forward, as the overlap only between A and C is 0.00

NoeticImbecile · Answer

I can't see the diagram

chetan2u · Answer

I hope it is visible now.

Fish181 · Answer

1) Take proportion who had read all three books and divide it by each total proportion by book.

P(A) .38/.58 = 65.5%

P(B) .38/.81 = 47%

P(C) .38/.72 = 53%

Part 1, answer is Book A.

2) We see in the venn diagram that where B and C overlap, it equals 0.00. Therefore 0%.

Kashu18 · Answer

We don't need to get into the specific calculations for this one. 
The question is:  Among the respondents who had read  {book name} , the probability that one selected at random had read all three books is greater than 0.60.

Which wants the probability to be "greater than" a specific number; i.e, the base should be as small as possible. As the base for A (0.58) is the smallest, it's the answer.

A certain publishing company surveyed readers of three books it publi

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A certain publishing company surveyed readers of three books it publi