Data Sufficiency

A jar contains 8 red marbles and y white marbles. If Joan takes 2 random marbles from the jar, is it more likely that she will have 2 red marbles than that she will have one marble of each color?

(1) y ≤ 8
(2) y ≥ 4

let's put the probability of selecting both red marbles:
{8 / (8+y)}{7/(7+y)}

probability of 1 of each color:
{8 / (8+y)}{y/(7+y)}

what you need to find out in this question is:
{8 / (8+y)}{7/(7+y)} > {8 / (8+y)}{y/(7+y)} which means

56 / {(8+y)(7+y)} > 8y / {(8+y)(7+y)} which means
56 > 8y which means
7 > y that is Is y < 7?

stmnt 1: y ≤ 8 clearly insuff; cross off A D
stmnt 2: y ≥ 4 also insuff; cross off B

together we have 4 <= y <= 8; also insuff as y could still be 8; cross off C

Answer E

What is OA and OE?

Hope this helps...

Let total number of possible ways of selecting any 2 marbles be 'S'.

probability of selecting 2 red marbles=8C2/S=28/S. ......(i)

probability of selecting 1 red and 1 white marble=8C1*YC1/S. ...... (ii)

Now if Y>=4 then YC1=4C1=4 which will render (ii) greater than (i).

Statement (1): Y<=8 . No sufficient as Y can be 2 or 8

Statement (2): Y>=4 . Sufficient as Y is >=4

beatthegmat.garry wrote:Let total number of possible ways of selecting any 2 marbles be 'S'.

probability of selecting 2 red marbles=8C2/S=28/S. ......(i)

probability of selecting 1 red and 1 white marble=8C1*YC1/S. ...... (ii)

Now if Y>=3 then YC1=3C1=3 which will render (ii) greater than (i).

Statement (1): Y<=8 . No sufficient as Y can be 2 or 8

Statement (2): Y>=4 . Sufficient as Y is >=3

Hi,
Almost correct but minor error. For y=3, (ii) is not greater than (i)
For y>=4, (ii) > (i)
Is 28/S > 8y/S? => Is y<7/2
So, if y<=3, the answer is yes
if y>=4, answer is No.
statement(2) is sufficient

Hence, B

Thanks Frankenstein

Yes indeed.

let's put the probability of selecting both red marbles:
{8 / (8+y)}{7/(7+y)}

probability of 1 of each color:
{8 / (8+y)}{y/(7+y)}

what you need to find out in this question is:
{8 / (8+y)}{7/(7+y)} > {8 / (8+y)}{y/(7+y)} which means

56 / {(8+y)(7+y)} > 8y / {(8+y)(7+y)} which means
56 > 8y which means
7 > y that is Is y < 7?

This is wrong.

probability of 1 of each color:
{8 / (8+y)}{y/(7+y)}

this should be -
2{8 / (8+y)}{y/(7+y)}

so is y < 3.5

clearly stmnt 2 is the winner.

Thanks guys...

OA: B