Data Sufficiency

Please Help

Is it E ?

P(W / E) = P(W) + P(E) - P(W&E)

1 - insufficient. we just know P(W&E) = 0. We don't know P(W) or P(E)

2 - insufficient. Knowing P(W) - P(E) will not help.

Together, we still don't know P(W) and P(E). So, E ?

Jay, I have been looking to get some notes on probability (and permutation/combination) formulas. I saw this question and was completely stumped to how to approach it. I have read the Kaplan book and Princeton Review till this point and none of them have anything regarding this. Do you have a resource in mind?

Thanks a lot.

.. take a look at the gmat resources section on the top ... it has some material for PnC ... u an indian ... if so then i can suggest some good books for PnC that are available in india ...

Thanks gabriel. I do not live in India, so can't use those books. I will have to do with online resources!

Let probability of one of the events be x and the other be y. the question is to calculate xy

from Statement 1, we obtain x+y = 0
from statement 2, we obtain x-y = 2

we can calculate x and y , where x = 1 and y = -1

so, theoretically, C is the answer as xy - -1.

But i do not understand what a probablility of -1 signifies in the physical world. Hence, I would Pick E.

btw what is the OA ?

arunjithp wrote:Let probability of one of the events be x and the other be y. the question is to calculate xy

from Statement 1, we obtain x+y = 0
from statement 2, we obtain x-y = 2

we can calculate x and y , where x = 1 and y = -1

so, theoretically, C is the answer as xy - -1.

But i do not understand what a probablility of -1 signifies in the physical world. Hence, I would Pick E.

probability of any event varies between 0 and 1 ... so -1 means nothing in the physical world or in the mathematical world ...

... jay has got it right ... the first statement says that p(xy)=0 ... it doesnt say anything about p(x)+p(y) .. so ur interpretation of the 1st statement is wrong ...

gabriel wrote:

arunjithp wrote:Let probability of one of the events be x and the other be y. the question is to calculate xy

from Statement 1, we obtain x+y = 0
from statement 2, we obtain x-y = 2

we can calculate x and y , where x = 1 and y = -1

so, theoretically, C is the answer as xy - -1.

But i do not understand what a probablility of -1 signifies in the physical world. Hence, I would Pick E.

probability of any event varies between 0 and 1 ... so -1 means nothing in the physical world or in the mathematical world ...

... jay has got it right ... the first statement says that p(xy)=0 ... it doesnt say anything about p(x)+p(y) .. so ur interpretation of the 1st statement is wrong ...

Here is what I was thinking, please correct me if I am wrong anywhere:

p(w) = probability of the ball being white
p(e) = probability of the ball being even.

p(w or e) = p(w) + p(e) - p(w and e) .............. (a)


p(e) = 12/25... if the balls are sequentially numbered from 1 thru 10 repetitively (assumption on my part, correct me if I am wrong)

(1) p(w and e) = 0, doesn't tell us anything about p(w)

(2) says p(w) - p(e) = 0.2 = 5/25
implies, p(w) - 12/25 = 5/25
implies, p(w) = 17/25
withouth knowing p(w and e) we can go nowhere with this info.

Take together, plug into eq (a)
p(w or e) = 17/25 + 5/25 - 0 = 22/25

Hence, SUFF taken together... ANSWER [C]

Hi,

First statement basically says us there is not a single ball with white color and even number painted on it.

Now the way you counted says us out of 25 balls 17 are white (since P(W) = 17/25) which means balls with the even number painted on it can be 8 only and that makes P(e) = 8/25. But intially we assumed it as 12/25...!!!! And then only concluded 17/25 figure.

Still I am not able to figure out exact problem with your solution. But something is wrong.

Let see if any one else can help us...

One more thing,

Take together, plug into eq (a)
p(w or e) = 17/25 + 5/25 - 0 = 22/25

Here you took P(e) = 5/25....It should be 12/25...5/25 is actully P(w) - P(e)

And on taking

P(e) = 12/25, P(w or e) comes to 29/25....which is wrong..

sorry dude......but some problem in your assumption..

.. of course something is wrong with the assumption .. bcoz the question never mentions any particular pattern of numbering of the balls .. so you can't assume any pattern ..

.. so the assumption that the balls are numbered repetitively from 1 to 10 does not hold ..

... and come on guyz.. isnt the most important rule in a DS that ur not supposed to assume anything that cannot be derived from the question or the statements that follow ...

gabriel wrote:.. of course something is wrong with the assumption .. bcoz the question never mentions any particular pattern of numbering of the balls .. so you can't assume any pattern ..

.. so the assumption that the balls are numbered repetitively from 1 to 10 does not hold ..

... and come on guyz.. isnt the most important rule in a DS that ur not supposed to assume anything that cannot be derived from the question or the statements that follow ...

You are right UmanG... my assumption was wrong, you just proved it with mathematical reasoning...

I am not sure how else to approach this problem. [E] anyone?