Every passenger on a certain airplane is from either Japan

Question

Every passenger on a certain airplane is from either Japan or Australia; no one is from both. Every passenger is reading either a novel or a biography; no one is reading both. If a passenger is to be selected at random, is the probability that the passenger is both from Japan and reading a novel greater than the probability that the passenger is both from Australia and reading a biography.

(1) The probability that a randomly selected passenger is either from Japan or reading a novel or both is 208/251 .

(2) The probability that a randomly selected passenger is either from Australia or reading a biography or both is 172/251

KarishmaB · Accepted Answer

You needn't give the standard 5 options for DS questions. They are the same for every question and people know them.

Make a table:

....................Japan...........Australia
Novel.............JN....................AN
Biography.......JB.....................AB

We need to know whether JN is greater than AB. JN represents number of people from Japan and reading a novel. AB represents number of people from Australia and reading a Biography and so on.
JN + AN + JB + AB = total number of people

(1) The probability that a randomly selected passenger is either from Japan or reading a novel or both is 208/251.

....................Japan...........Australia
Novel.............JN.....................AN
Biography......JB.....................AB

JN + AN + JB represent the passengers who are either from Japan or reading a novel or both. They sum up to 208 if total number of passengers is 251. This means AB = 251 - 208 = 43. But we don't know the value of JN so we cannot compare JN with AB.

(2) The probability that a randomly selected passenger is either from Australia or reading a biography or both is 172/251.
....................Japan...........Australia
Novel.............JN.....................AN
Biography......JB......................AB

AN + AB + JB = 172
So JN = 251 - 172 = 79
We don't AB so statement 2 alone is not sufficient to answer.

Using both statements we know AB = 43 and JN = 79 so JN is greater. Sufficient.
Answer (C)

blueseas · Answer

Hi,
 lets take total passenger be 251 
 Jb =japanese reading biography
 Jn =japanese reading novel
 Ab =australian reading biography
 An =australian reading novels

we have deter mine whether is the probability that the passenger is both from Japan and reading a novel greater than the probability that the passenger is both from Australia and reading a biography.
or in short
 whether Jn>Ab 
Jb+Jn+Ab+An=total=251
statement 1:
Japan or reading novel or both = all japanese and all who read novel= Jn+Jb+An=208.....(as probabity is 208/251)
this gives Ab=251-208=43....BUT WE CANNOT DETERMINE what is the share of Jn in 208
hence insufficient

statement 2:
Australia or reading a biography or both= all australians and all who read biography=Ab+An+Jb=172...(as probability is 172/251)
same as statement 1 this is insuffficient as we will be unable to take out Ab
hence insufficient

now subtract those two equations..
you will get Jn+Jb+An-Ab-An-Jb=208-172=36
or Jn-Ab=36
clearly Jn>Ab...hence probability of Jn will be more..
hence sufficient..

hope it helps

zerosleep · Answer

Hello all,

I am extremely sorry if this is not the correct place to ask but I could not find any other suitable section, so I am asking my query here. 
Can someone(quant experts) please help me on probability - concepts and questions. I am quite good in other areas including permutation and combination.
 My weaknes in probability is I do not know the resources to refer to improve my understanding and solve tough intermediate and tough problems.

Please guide since probability questions are most likely to come as the score increases.

Thanks.!!

Bunuel · Answer

Theory on Combinations: math-combinatorics-87345.html DS questions on Combinations: search.php?search_id=tag&tag_id=31 PS questions on Combinations: search.php?search_id=tag&tag_id=52 Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html Theory on probability problems: math-probability-87244.html All DS probability problems to practice: search.php?search_id=tag&tag_id=33 All PS probability problems to practice: search.php?search_id=tag&tag_id=54 Tough probability questions: hardest-area-questions-probability-and-combinations-101361.html Hope it helps.

GIGMAT · Answer

i do not understand why you say "JN + AN + JB represent the passengers who are either from Japan or reading a novel or both" . Shouldn't it be (JN+JB) + (JN+AN) + (JN) , which makes it 3JN+AN+JB. Please help!

KarishmaB · Answer

You are counting instances, not people. We need the number of people instead.

JN is the number of people who are Japanese and reading novels. JB is the number of people who are Japanese and reading biographies. Total JN and JB account for all Japanese.
AN is the number of Aussies reading novels. AB is the number of Aussies who are reading biographies. AN + AB account for all Aussies.

JN+JB+AN+AB account for all people in the plane.

Number of people who are either from Japan or reading a novel or both includes all people on the plane except Aussies who are reading biographies. 
So JN+JB+AN represents the number of people who are either Japanese or reading a novel or both.

You have double/triple counted the people.

KrishnakumarKA1 · Answer

Solution: 
Let’s take the abbreviation for 
Japanese reading Novel as  JN 
Japanese reading Biography as  JB 
Australian reading Novel as  AN 
Australian reading Biography as  AB 
 To find:  Is the probability that the passenger is both from Japan and reading a novel greater than the probability that the passenger is both from Australia and reading a biography?
Basically, the question is  JN > AB?

Analysis of statement 1:  The probability that a randomly selected passenger is either from Japan or reading a novel or both is 208/251
Let’s take the total i.e.  JN+JB+AN+AB=251-------(1) 
As the probability given for the selected passenger is either from Japan or reading a novel or both is 208/251
∴Total number of Japanese passengers + Passengers reading novel + Number of Japanese passengers who are reading novel =  JN+JB+AN=208-----(2)  
  . 
From equations 1 and 2 we get; 
 AB = 251 – 208 = 43. 
As in equation 2, we cannot determine the value of JN. Hence we cannot compare the values of JN and AB. 
So, statement 1 is not sufficient to answer. We can eliminate options A and D.

Analysis of statement 2:  The probability that a randomly selected passenger is either from Australia or reading a biography or both is 172/251
Let’s take the total i.e.  JN+JB+AN+AB=251-------(1) 
As the probability given for the selected passenger is either from Australia or reading a biography or both is 172/251
∴Total number of Australian passengers + Passengers reading biography + Number of Australian passengers who are reading Biography=  AB+AN+JB=172-----(2) 
From equations 1 and 2 we get; 
 JN = 251 – 172 = 79. 
As in equation 2, we cannot determine the value of AB. Hence we cannot compare the values of JN and AB. 
So, statement 2 is not sufficient to answer. We can eliminate option B.

Combining the statements 1 and 2 we get; 
From statement 1 we get;  AB = 43 
From statement 2 we get;  JN = 79 
By comparing the values of AB and JN, it is clear that  JN > AB.  
Hence the probability that the passenger is both from Japan and reading a novel greater than the probability that the passenger is both from Australia and reading a biography.

The correct answer option is “C”.

bumpbot · Answer

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Every passenger on a certain airplane is from either Japan

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