Question

A BAG CONTAINS 3 RED CHIPS, 2 BLUE CHIPS AND 1 WHITE CHIP. IF 2 CHIPS ARE CHOSEN FROM THE BAG WITHOUT REPLACEMENT DETERMINE THE PROBABILITY THAT THEY ARE OF DIFFERENT COLORS

Answer 1

You can calculate the different combinations to get different colours, but you can also calculate the probability P of getting the same colours, and the required probability is 1-P.

get two reds: (3/6)*(2/5)=1/5
get two blues: (2/6)*(1/6)=1/18
Probability of getting two reds or two blues: (1/5)+(1/18)=23/90
Probability of not getting two of the same colour = 1-(23/90)=67/90