Calculate Total marbles:
Total marbles = Blue + Red + Green
Total marbles = 3 + 4 + 5
Total marbles = 12
Probability of a green = 5/12
Probability of not green = 1 - 5/12 = 7/12
To get exactly one green in two draws, we either get a green, not green, or a not green, green
First Draw Green, Second Draw Not Green
1st draw: Probability of a green = 5/12
2nd draw: Probability of not green = 7/11 <-- 11 since we did not replace the first marble
To get the probability of the event, since each draw is independent, we multiply both probabilities
Probability of the event is (5/12) * (7/11) = 35/132
First Draw Not Green, Second Draw Not Green
1st draw: Probability of not a green = 7/12
2nd draw: Probability of not green = 5/11 <-- 11 since we did not replace the first marble
To get the probability of the event, since each draw is independent, we multiply both probabilities
Probability of the event is (7/12) * (5/11) = 35/132
To get the probability of exactly one green, we add both of the events:
First Draw Green, Second Draw Not Green + First Draw Not Green, Second Draw Not Green
35/132 + 35/132 = 70/132
SO THE ANSWER IS 35/66
