Any easy way to solve this???

[hk]

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

[m&m]

by considering extremes the answer can either be C or E (in a whites can be 0, in b whites can be 1000000 making probability of 2 red virtually 0)

in C whites are between 4 and 8

if 8 then probability of 1 and 1 is 8/16*8/15
and probability of 2 reds is 8/16*7/15

so probability of 1 and 1 is higher

in 4 then probability of 1 and 1 is 8/12*4/11
and probability of 2 reds is 8/12*7/11

so probability of 2 reds is higher

so insuff therefore E

[hk]

Wow!!! The OA is C

I got it right as i plugged in number for value of y = 8,5,4,2 and got the right answer but wanted to know if anybody has an easier way!!!

btw m&m - try again..