in total there are 6,4,8 which equals 18 .There are 18 balls in total. but Alex removed 3 so now there are 15 balls. There 3 different colors and 15 balls. So there is a 5% out of 15 that you will get a certain color .To find the probability you need to calculate all the possible outcomes.
G=Green R=Red P=Purple
G,R,P
G,P,R
P,G,R
P,R,G
R,P,G,
R,G,P
There is 6 different outcomes, 15 balls and a 5% chance to get a certain color so if you want to exactly get G,R,P there is a (15 divided by 6) chance to get that order.
(I'm not good at calculating that part.)