# There is a bag filled with 3 blue, 4 red and 5 green marbles. A marble is taken at random from the

Discussion in 'Calculator Requests' started by math_celebrity, Jun 28, 2019.

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There is a bag filled with 3 blue, 4 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?

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

Using our fraction simplify calculator, we get:
35/66