DS - Prob. difficult question

[karthikpandian19]

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.

[eagleeye]

Hi karthikpandian19:

This is how I did it:
Let the probability that a person is from Japan be J. Similarly for Australia be A
Let the probability that a person is reading a novel be N. Similarly for Biography be A.
Since no one is from both countries and no one reads both ; we have AJ = 0 ; NB = 0.

Then A+J = 1; N+B =1 (Since P(AuB) = P(A)+P(B)-P(AB)

Now we need to find out whether JN > AB

1) We are given that we select either someone from Japan, or someone who reads a novel or does both.
In other words we need to find J or N or both.
Now we know that:
J = J(N+B) = JN + JB (Note that we could also have arrived at this statement since people from Japan includes both novel readers and biography readers).
similarly, N = N(A+J) = NA + NJ

We are given to find probability of people either from Japan or Novel people or both.

In other words we have JN + JB + NA (note that since Japanese Novel readers are in both sets, we count it only once). We then have JN + JB + NA = 208/251;
Now JN+ JB + NA+ (BA) = J + A = 1
Then, BA = 1 - (JN+JB+NA) = 1-208/251 = 43/251. We don't know what JN is. Hence not sufficient.

2) With similar reasoning as above; we have AB+AN + JB = 172/251 and JN = 1 - (AB + AN + JB) = 1 -172/251 = 79/251; We only know JN from this statement; we don't know AB; Hence not sufficient.

However from both 1 and 2, we have JN = 79/251 and AB = 43/251, Clearly we can see that JN>AB. Hence, C is the correct choice.

Let me know if I got it right, and if this helps

[aneesh.kg]

Statement(1):



Statement(2):



Combining the two statements,



[spoiler](C)[/spoiler] is the correct answer.

[karthikpandian19]

........We then have JN + JB + NA = 208/251;
Now JN+ JB + NA+ (BA) = J + A = 1
Then, BA = 1 - (JN+JB+NA) = 1-208/251 = 43/251. We don't know what JN is. Hence not sufficient.

Here how u r adding BA? can you explain pls???