TIFR CSE 2010 | Part A | Question: 1

Question

A box contains $731$ black balls and $2000$ white balls. The following process is to be repeated as long as possible. Arbitrarily select two balls from the box. If they are of the same color, throw them out and put a black ball into the box ( enough extra black balls are available to do this). If they are of different color, place the white ball back into the box and throw the black ball away. Which of the following is correct?

• A. The process can be applied indefinitely without any prior bound
• B. The process will stop with a single white ball in the box
• C. The process will stop with a single black ball in the box
• D. The process will stop with the box empty
• E. None of the above

Answer 1

I think A.

Because 3 case BB,WW,BW. So in every case either 1Black ball or 1 white Ball is added. So Every time it will contain some pair.

White ball cannot be 1 beczits going in pair only and total no of white is even.