A bag contains 5 green marbles, 3 yellow marbles and 2 red marbles. What is the probability of picking three green marbles from the bag without replacement?
3/10 * 2/9 * 1/8 = 1/120
1/12
To calculate the probability of picking three green marbles from the bag without replacement, we need to first determine the total number of marbles in the bag.
The bag contains:
- 5 green marbles
- 3 yellow marbles
- 2 red marbles
So, the total number of marbles is 5 (green) + 3 (yellow) + 2 (red) = 10 marbles.
Now, let's calculate the probability step by step:
Step 1: Determine the probability of picking the first green marble.
Since there are 5 green marbles out of a total of 10 marbles, the probability of picking a green marble first is 5/10.
Step 2: Determine the probability of picking the second green marble.
After picking the first green marble, there will be 4 green marbles left out of a total of 9 marbles. Therefore, the probability of picking a second green marble is 4/9.
Step 3: Determine the probability of picking the third green marble.
After picking two green marbles, there will be 3 green marbles left out of a total of 8 marbles. Hence, the probability of picking a third green marble is 3/8.
Step 4: Calculate the overall probability.
To find the probability of all three events occurring (picking three green marbles), we multiply the individual probabilities together. So, the overall probability is (5/10) * (4/9) * (3/8) = 60/720 = 1/12.
Therefore, the probability of picking three green marbles from the bag without replacement is 1/12.