+479 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.
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
.
