SOLUTION: an urn contains 4 black marbles, 3 red marbles, and 5 green marbles. Three marbles are selected without replacement. Find the probability that at least one red marble is selected

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Question 844896: an urn contains 4 black marbles, 3 red marbles, and 5 green marbles. Three marbles are selected without replacement. Find the probability that at least one red marble is selected
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at all of the combinations that don't have R in them and calculate the probabilities
BBB=4%2A4%2A4%2F12%5E3=64%2F1728
BBG=4%2A4%2A5%2F12%5E3=80%2F1728
BGB=4%2A5%2A4%2F12%5E3=80%2F1728
BGG=4%2A5%2A5%2F12%5E3=100%2F1728
GBB=5%2A4%2A4%2F12%5E3=80%2F1728
GBG=5%2A4%2A5%2F12%5E3=100%2F1728
GGB=5%2A5%2A4%2F12%5E3=100%2F1728
GGG=5%2A5%2A5%2F12%5E3=125%2F1728
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P%28at+least+1+R%29%2BP%28no+R%29=1
P%28no+R%29=%2864%2B3%2A80%2B3%2A100%2B125%29%2F1728=729%2F1728
P%28at+least+1+R%29=1-729%2F1728
P%28at+least+1+R%29=999%2F1728
P%28at+least+1+R%29=111%2F192