Question

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 replaced. Another marble is taken at random. What is the probability of getting 2 different colours?

Answer 1

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