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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?

Feb 16, 2020

#1
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The probability is 4/17.

Feb 16, 2020
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Guest Feb 16, 2020
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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)

Feb 16, 2020