Every passenger on a certain airplane is from either Japan

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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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.!!

Hope it helps.

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!

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.

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 = \(JN+JB+AN=208-----(2)\)
[NOTE: Here we have to be careful as we can count JN twice].
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”.

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