math problem what is best answer

Question

In a giant bin, we stir together 2019 red jelly beans and 2019 green jelly beans. We pull 3 jelly beans out of the bin at a time. There are two possibilities – they are all the same color or there are 2 of one color (and one of the other). In the first case (3 of the same color), we eat all 3 jelly beans. In the second case (2 of one color), we put 1 jelly bean back of the majority color and eat the other 2. 

If we repeat this process until there are fewer than 3 jelly beans left in the bin, there are these possibilities 

1.    No jelly beans. 

2.    One red jelly bean. 

3.    One green jelly bean. 

4.    Two red jelly beans. 

5.    Two green jelly beans. 

6.    One red and one green jelly bean

Which of these outcomes is most likely? Which is least likely? 

Answer 1

Thinking through this problem in terms of differences between starting values helps to simplify it dramatically. Consider different starting conditions: what if there are two more reds than greens? What are the possible outcomes then? Make sure to watch the video in high quality so that you can read the code. I've pasted the code below, which you can fiddle around with on an online IDE should you please:

class Main {

public static void main(String[] args) {

int none = 0, oneRed = 0, oneGreen = 0, twoRed = 0, twoGreen = 0, oneEach = 0;

for (int y = 0; y < 1000; y++) {

int greens = 2018, reds = 2019;

while (greens + reds >= 3) {

int redsDrawn = 0;

double proportionReds = (double) reds / (reds + greens);

for (int x = 0; x < 3; x++) {

if (Math.random() <= proportionReds && reds > 0) {

redsDrawn++;

reds--;

} else if (greens > 0)

greens--;

else {

reds--;

redsDrawn++;

}

}

if (redsDrawn == 1)

greens++;

else if (redsDrawn == 2)

reds++;

}

if (reds == 2)

twoRed++;

else if (reds == 1) {

if (greens == 0)

oneRed++;

else if (greens == 1)

oneEach++;

} else if (reds == 0) {

if (greens == 1)

oneGreen++;

else if (greens == 2)

twoGreen++;

else if (greens == 0)

none++;

}

}

System.out.print("None: " + none + "\nOne Red: " + oneRed + "\nOne Green: " + oneGreen + "\nTwo Red: " + twoRed

+ "\nTwo Green: " + twoGreen + "\nOne Each: " + oneEach);

}

}