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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