Final answer:
To guarantee having 3 balls of each color from 95 green and 90 red balls, 96 balls need to be taken out. This ensures that, in the worst-case scenario, you have drawn either all green or all red balls first, leaving only the opposite color to be drawn by the 96th pick.
Step-by-step explanation:
A student has asked how many balls we need to take out from a total of 95 green balls and 90 red balls to ensure getting 3 of each color. In the worst-case scenario, you could pick out all 95 green balls before getting to the red balls. But, since you want 3 red balls, as soon as you have picked 3 red balls, you can stop. Similarly, in the worst-case scenario for green balls, you might pick all 90 red balls before getting to the greens. But again, you only need 3 green balls.
So, in the worst-case scenario, you could pick out 95 green balls then 3 red balls, or 90 red balls then 3 green balls. Therefore, a safe number to ensure you have 3 of each color would be 95 + 3 or 90 + 3, which are both 98.
However, the minimum number we need to take out to guarantee 3 balls of each color is 96 balls. This is because after taking out 92 balls, there will be only 3 green or 3 red balls left in the worst case, and then we will be forced to choose the 3 remaining balls of the other color by the 96th draw.