A bag contains 1 red, 2 blue, and 3 green marbles. Two marbles are removed without replacement. The probability tree shows the possible outcomes.
The compound probability of each outcome.
There are a total of 6 marbles in the bag, and we are taking out two marbles without replacement. So there are a total of 6*5 = 30 possible combinations of marbles.
Each outcome can be found by multiplying the probability of each individual event.
1. Red and then Blue: (1/6) * (2/5) = 1/15
2. Red and then Green: (1/6) * (3/5) = 1/10
3. Blue and then Red: (2/6) * (1/5) = 1/15
4. Blue and then Green: (2/6) * (3/5) = 1/5
5. Green and then Red: (3/6) * (1/5) = 1/10
6. Green and then Blue: (3/6) * (2/5) = 1/5
In summary:
1. Red and Blue: 1/15 + 1/15 = 2/15
2. Red and Green: 1/10 + 1/10 = 1/5
3. Blue and Green: 1/5 + 1/5 = 2/5