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Every passenger on a certain airplane is from either Japan

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Every passenger on a certain airplane is from either Japan [#permalink] New post 15 Jul 2013, 07:49
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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
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Re: Every passenger on a certain airplane [#permalink] New post 15 Jul 2013, 08:22
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vibhav wrote:
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


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
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Re: Every passenger on a certain airplane [#permalink] New post 15 Jul 2013, 09:35
shailesh, now it all makes sense! thnx!
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Probability [#permalink] New post 02 Dec 2013, 13:27
Qs:

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 .

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


a!Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.


b!Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.


c!BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.


d!EACH statement ALONE is sufficient.


e!Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: Probability [#permalink] New post 02 Dec 2013, 20:35
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Expert's post
garry_arora2000 wrote:
Qs:

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 .

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



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)
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Re: Probability [#permalink] New post 03 Dec 2013, 00:42
Expert's post
garry_arora2000 wrote:
Qs:

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 .

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


a!Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.


b!Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.


c!BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.


d!EACH statement ALONE is sufficient.


e!Statements (1) and (2) TOGETHER are NOT sufficient.


Merging similar topics.

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Re: Every passenger on a certain airplane is from either Japan [#permalink] New post 03 Dec 2013, 11:44
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.!!
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Re: Every passenger on a certain airplane is from either Japan [#permalink] New post 04 Dec 2013, 01:31
Expert's post
zerosleep wrote:
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.!!


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.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Every passenger on a certain airplane is from either Japan   [#permalink] 04 Dec 2013, 01:31
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