There is a bag filled with 4 blue, 3 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 green
2 cases: green then non-green OR non-green then green
Prob(your stated event) = (7/12)(5/11) + (5/12)(7/11) = 70/132
= 35/66
To calculate the probability of getting exactly 1 green marble, we need to first determine the total number of marbles and the number of favorable outcomes.
Total number of marbles = number of blue marbles + number of red marbles + number of green marbles
Total number of marbles = 4 + 3 + 5 = 12
Favorable outcome: Getting exactly 1 green marble
To calculate the probability, we need to consider two scenarios:
Scenario 1: The first marble drawn is green and the second is not green.
Probability of drawing a green marble = (Number of green marbles / Total number of marbles) = 5/12
For the second marble, since the first green marble was already drawn and not replaced, the number of green marbles becomes (5 - 1) = 4, and the total number of marbles becomes (12 - 1) = 11.
Probability of not drawing a green marble in the second draw = (Number of non-green marbles / Total number of marbles) = (7/11)
Scenario 2: The first marble drawn is not green, and the second marble is green.
Probability of drawing a non-green marble = (Number of non-green marbles / Total number of marbles) = 7/12
For the second marble, since the first marble is not green, the number of green marbles remains 5, and the total number of marbles becomes (12 - 1) = 11.
Probability of drawing a green marble in the second draw = (Number of green marbles / Total number of marbles) = 5/11
To obtain the probability of getting exactly 1 green marble, we add the probabilities from both scenarios:
Probability = (Probability of Scenario 1) + (Probability of Scenario 2)
Probability = [(5/12) * (7/11)] + [(7/12) * (5/11)]
After calculating this expression, we find that the probability of getting exactly 1 green marble is 0.318 (rounded to three decimal places) or approximately 31.8%.