Question

We have a bag filled with 201 marbles, of which 100 of them are blue and 101 of them are red. Every turn, we remove 2 marbles from the bag. If the two marbles are of the same color, we remove the two marbles but add a blue marble into the bag. If the two marbles are of different colors, we remove the two marbles and add a red marble into the bag. What is the color of the last marble in the bag?

Answer 1

Last color of the marble in the bag is RED.

When you choose 2 different marble , at that time the no. of red marbles in the bag will not change as we are adding a red marble.

Since there are 101 red marbles , it cannot be completely become zero as removing 2 red marbles will result in atleast 1 red marble remaining at the end.

AT the end of all simulations you will find yourselves with 1 blue and 1 red marble and when you draw 1 red and 1 blue , you add one red marble and then red marble is the last in bag.

For any simulations ,at the end there will be a single red marble.