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

Statement 1

Let's assume y=8
P(Two Red marbles) = 8/16*7/15
P(One Red and One white marble) = 2(8/16*8/15)
In this case P(Two red marbles) < P(One Red and One White marble)
When y =1
P(Two red marbles) = 8/9*7/8
P(One Red and One white marble) = 2(8/9*1/8)
In this case P(Two red marbles) > P(One Red and One White marble). Insufficient

Statement 2

Let's assume y=4
P(Two Red marbles) = 8/12*7/11
P(One Red and One White marble) = 2(8/12*4/11)
In this case P(Two Red marbles) < P(One Red and One White marble)
We have already seen a case where y=8. i.e, as y increases we are certain that we will have only
one answer. Sufficient

Hi sl750,

Why have you taken P(One Red and One white marble) = 2(8/16*8/15) . Why the multiple of 2? Whichever way red and white marbles are picked, the likelihood of the event to occur will not change

That is required because we can pick either the Red marble first or the White marble first, the order is not specified. This problem involves selection and probability