Answer :
Final answer:
To solve this problem, set up a system of equations and solve simultaneously for the number of red and green counters originally in the bag.
Explanation:
To solve this problem, we can set up a system of equations.
Let r be the number of red counters and g be the number of green counters originally in the bag.
According to the given information, the probability of getting a green counter on the first draw is 4/9.
So, the equation is (g/(r+g)) = 4/9.
After putting the counters back in the bag and adding more counters, the probability of getting a green counter on the second draw is 10/23.
So, the equation is ((g+2)/(r+g+6)) = 10/23.
Now, we can solve these equations simultaneously to find the values of r and g.
The solution to the system of equations is r = 5 and g = 9.