l An urn contains 9 red marbles 7 white marbles and 5 blue m

l. An urn contains 9 red marbles, 7 white marbles, and 5 blue marbles. You grab 4 of the marbles. What is the probability that:

1. 2 of the marbles are white and the other 2 are blue?

2. They are not all of the same color?

3. At least 3 are red?

Given that 9 red marbles, 7 white marbles, 5 blue marbles

Total number of events is 21C₄ = (21)!/(21-4)!(4)! = 5985

P(E) = (7C₂)(5C₂)/21C₄ =(21*10)/5985= 210/5985 =0.0351

Let us consider that all are same colour then we have

P(all the marbles are of same colour) = 9C₄/21C₄ = 126/5985 = 0.0211

P(all the marbles are not of same colour) = 1- 0.0211 = 0.9789

P(all the marbles are of same colour) = 7C₄/21C₄ = 35/5985 =0.0058

P(all the marbles are not of same colour) = 1- 0.0085 =0.9942

P(all the marbles are of same colour) = 5C₄/21C₄ = 5/5985 = 0.0008

P(all the marbles are not of same colour) = 1- 0.0008 = 0.9992

P(3 are red and 1 is white) = (9C₃)(7C₁) /21C₄ = 84*7/5985 =0.0982

P(3 are red and 1 is blue) = (9C₃)(5C₁) /21C₄ = 84*5/5985 =0.0702