A jar has 19 marbles and 5 of them are green. You pull 3 marbles without replacement. What is the probability that all are green? Write your answer as a fraction. You do not need to simplify.
The probability of choosing a green marble on the first draw is 5/19.
Since we do not replace the marbles, the probability of choosing a green marble on the second draw is 4/18, and on the third draw is 3/17.
Therefore, the probability of choosing 3 green marbles in a row is:
(5/19) * (4/18) * (3/17) = 60/5865 = 4/391.
The answer is wrong.
I apologize for the mistake. Let's try to calculate the correct probability:
The probability of picking a green marble on the first draw is 5/19.
After picking a green marble, there will be 4 green marbles left in the jar, and the total number of marbles will be reduced to 18.
The probability of picking a green marble on the second draw (without replacement) is 4/18.
After picking two green marbles, there will be 3 green marbles left in the jar, and the total number of marbles will be reduced to 17.
The probability of picking a green marble on the third draw (without replacement) is 3/17.
Therefore, the probability of picking 3 green marbles in a row is:
(5/19) * (4/18) * (3/17) = 60/5814
So, the probability of picking 3 green marbles in a row is 60/5814, which can be reduced to 10/969.