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Three marbles are randomly selected, without replacement, from a bag containing two red, two blue and two green marbles. What is the probability that one marble of each color is selected? Express your answer as a common fraction.

 Oct 2, 2020
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Three marbles are randomly selected, without replacement, from a bag containing two red, two blue and two green marbles. What is the probability that one marble of each color is selected? Express your answer as a common fraction.  

 

The first marble can be anything.  

The probability of pulling out one is 1.               the probability of this happening is 1                                         (1)  

 

There are 5 marbles left and 4 of them   

are suitable.  The probability of pulling

out one of those four is 4/5.                               the probability of this and (1) happening is 1 • 4/5 = 4/5            (2)  

 

There are 4 marbles left and 2 of them  

are suitable.  The probability of pulling  

out one of those two is 2/4.                                the probability of this and (2) happening is 1 • 4/5 • 2/4 = 8/20   (3)   

 

Reducing the fraction in (3) to lowest terms, the probability of getting one of each color is 2/5  

.

 Oct 2, 2020

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