A bag contains 19 red balls and 19 black balls. Two balls are removed at a…
2017
A bag contains 19 red balls and 19 black balls. Two balls are removed at a time repeatedly and discarded if they are of the same colour, but if they are different, black ball is discarded and red ball is returned to the bag. The probability that this process will terminate with one red ball is
- A.
1
- B.
1/21
- C.
0
- D.
0.5
Attempted by 46 students.
Show answer & explanation
Correct answer: A
Let R be the number of red balls and B be the number of black balls. Initially, R = 19 (odd).
Consider the effect of each draw on R: (1) Two reds discarded: R decreases by 2. (2) Two blacks discarded: R unchanged. (3) One red, one black: Black discarded, Red returned, so R unchanged.
In all cases, the parity (odd/even nature) of R remains invariant. Since we start with an odd number (19), the final count of red balls must be odd.
The process terminates when fewer than two balls remain. Since the red count must be odd, it cannot be 0. Thus, exactly one red ball remains with probability 1.