Solution:Let’s take the abbreviation for
Japanese reading Novel as
JNJapanese reading Biography as
JBAustralian reading Novel as
ANAustralian reading Biography as
ABTo 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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