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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