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There are exactly three types of newspapers in country Z: Newspaper A,

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chetan2u
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There are exactly three types of newspapers in country Z: Newspaper A, [#permalink] New post   26 Feb 2024, 05:36
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53% (03:17) correct 47% (03:06) wrong based on 128 sessions
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Data Insights (DI) Butler 2024 [ Date: 26-Feb-2023] 


There are exactly three types of newspapers in country Z: Newspaper A, Newspaper B, and Newspaper C, and every citizen reads at least one of these three newspapers.
An initial analysis by an agency on ­the number of citizens and the newspaper they read is given below.

A second study that carried out the survey in detail reported the following:-
1. The number of people who read newspaper B were correct.
2. The number of people who read newspaper C were also correctly determined by the initial analysis. However, all those who read newspaper C also read newspaper A.


The survey was finally released after taking above two points in consideration. Select the correct option from the dropdown menu based on the final survey released.

A. If one citizen is randomly selected from the newspaper readers above, the probability that a person reads exactly two of the newspapers is .

B. The percentage of population not reading newspaper A is approx .


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Dropdown 1: 10/24 Dropdown 2: 21
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There are exactly three types of newspapers in country Z: Newspaper A, [#permalink] New post   27 Feb 2024, 04:15
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The initial analysis:
Only A - 7
Only B - 5
Only C - 5
Only (B&C) - 1
Only (B&A) - 2
Only (C&A) - 3
All three - 1

Final Survey:
All those who read C also read A, so wherever C is there, A gets added. Changes in Red
Only C - 5 becomes Only (C&A)
Only (B&C) - 1 becomes All three
Because of above the new distribution will be
Only A - 7
Only C - 5-5 = 0
Only B - 5
Only (C&B) - 1-1 = 0
Only (C&A) - 2+5 = 7
Only (B&A) - 3
All three - 1+1 = 2

A. If one citizen is randomly selected from the newspaper readers above, the probability that a person reads exactly two of the newspapers is 
Exactly two = Only (B&C) + Only (B&A) + Only (A&C) = 0+3+7 = 10. Hence P = \(\frac{10}{24}\)

B. The percentage of population not reading newspaper A is approx 
'Only B' are the ones not reading A => Hence P = \(\frac{5}{24}*100=20.83\) ~ 21%­
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There are exactly three types of newspapers in country Z: Newspaper A, [#permalink] New post   27 Feb 2024, 22:36
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chetan2u wrote:
The initial analysis:
Only A - 7
Only B - 5
Only C - 5
Only (B&C) - 1
Only (B&A) - 2
Only (C&A) - 3
All three - 1

Final Survey:
All those who read B also read A, so wherever B is there, A gets added. Changes in Red
Only B - 5 becomes Only (B&A)
Only (B&C) - 1 becomes All three
Because of above the new distribution will be
Only A - 7
Only B - 5-5 = 0
Only C - 5
Only (B&C) - 1-1 = 0
Only (B&A) - 2+5 = 7
Only (C&A) - 3
All three - 1+1 = 2

A. If one citizen is randomly selected from the newspaper readers above, the probability that a person reads exactly two of the newspapers is 
Exactly two = Only (B&C) + Only (B&A) + Only (A&C) = 0+7+3 = 10. Hence P = \(\frac{10}{24}\)

B. The percentage of population not reading newspaper A is approx 
Only C are the ones not reading A => Hence P = \(\frac{5}{24}*100=20.83\) ~ 21%
 

­As per question stem-2
2. The number of people who read newspaper C were also correctly determined by the initial analysis. However, all those who read newspaper C also read newspaper A.
chetan2u Shouldn't C and A be considered instead of B and A ? Pleae pardon me if my below reasoning is incorrect.
a) Only C moves to only(A and C), which becomes 3 + 5 = 8
b) Only(B and C) moves to (A and B and C) = 1+1 = 2

For first prompt -
Exactly 2 = Only (B and A) and Only (C and A) = 2 + 8 = 10 ==> P(Exactly 2) = 10/24
For second prompt -
Not reading A = only B = 5  , which is equalt to ~21% of 24.­
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Re: There are exactly three types of newspapers in country Z: Newspaper A, [#permalink] New post   27 Feb 2024, 22:57
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Aryaa03

You are absolutely correct. That’s a typing error and was meant to be C only.
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Re: There are exactly three types of newspapers in country Z: Newspaper A, [#permalink] New post   29 Mar 2024, 11:19
Finding from 2nd study: All C are A
=> Those belong to only 2 groups C & A = 8 (instead of 3)
=> Those belong to all 3 gropus = 2 (instead of 1)

Counting the total (left to right, then top to bottom): 5 + 2 + 7 +1 + 1 + 3 + 5 = 24­

A. If one citizen is randomly selected from the newspaper readers above, the probability that a person reads exactly two of the newspapers is [10/24].

Those belong to only 2 groups A & B = 2
Those belong to only 2 groups A & C = 8
There are no one belong to only 2 groups B & C (because any one belonging to 2 groups B&C must also belong to group A)

Total number of those belongs to only 2 groups = 10 (=8+2)
Total number of people = 24

Probability = 10/24

B. The percentage of population not reading newspaper A is approx [21].

Those not reading A include only 5 people only belonging to group B
Total number of people = 24

Percentage = 5/24 = 20.8% = approx. 21%
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Re: There are exactly three types of newspapers in country Z: Newspaper A, [#permalink]
29 Mar 2024, 11:19
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