Question

An urn contains 5 red, 7 blue and 6 green marbles. If a set of 4 marbles is randomly selected, what is the probability that each of the marbles will be

(a) of the same color?

(b) of different colors?

Answer 1

Total marbles = 18

Total ways if drawing 4 marbles = 18 C4

(a) probability that each marble will be of same color = probability that all 4 marbles are red + probability that all 4 marbles are blue + probability that all 4 marbles are green = (5C4 + 7C4 + 6C4)/(18C4) = (5+35+15)/(3060) = 0.01797

(B) different color :

As there are only three color marbles that are present in the urn, and we are drawing 4 marbles. So we will never be able to draw all marbles of different color. ( Peigeonhol principle : atleast two marbles are of same color)

So probability = 0