Find the probability

Question

There are 25 red marbles, 15 green marbles, and 10 blue marbles.

You randomly pick 4 from the bag.

What is the probability of picking at least 1 marble of each color?

Answer 1

Hi Zimming, since you are randomly picking 4 marbles from the bag of 25 red + 15 green + 10 blue = 50 marbles, there are 3 different ways of getting at least 1 marble of each color:

1 red, 1 green, 2 blue w/ prob = (1/2) * (3/10) * (1/5)^2 = 3/500 = 0.006

1 red, 2 green, 1 blue w/ prob = (1/2) * (3/10)^2 * (1/5) = 9/1000 = 0.009

2 red, 1 green, 1 blue w/ prob = (1/2)^2 * (3/10) * (1/5) = 3/200 = 0.015

Thus the probability of picking at least 1 marble of each color is = 0.006 + 0.009 + 0.015 = 0.03