A bag contains 4 red marbles, 5 yellow marbles, and 6 blue marbles. Three marbles are to be picked out randomly (without replacement). What is the probability that exactly two of them have the same color?
+118608 A bag contains 4 red marbles, 5 yellow marbles, and 6 blue marbles. Three marbles are to be picked out randomly (without replacement). What is the probability that exactly two of them have the same color?
15 marbles. Let each one have a unique number, so in this sense, there are all different.
How many combinations are there
All red 4C3=4
All yellow 5C3=10
All blue 6C3=20
All the same colour=34
Exactly 2 red = 4C2*11 = 66
Exactly 2 yellow = 5C2*10=100
Exactly 2 blue = 6C2*9=135
Exactly 2 the same colour = 301
All different = 4*5*6=120
So
P(exactly two of them have the same color) = 301 /(23+301+120) = 301 / 444
(This is my logic, not necessarily correct)
