Pick marbles please

[saurabh2525_gupta]

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

[sl750]

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

[saurabh2525_gupta]

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

[sl750]

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