A bag contains 19 red balls and 19 black balls. Two balls are chosen 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

Step-by-step solution

3 different cases formed Case I : When both red balls are chosen, then both balls are removed from the bag. Case II : When both black balls are chosen, then both balls are again removed from the bag. Case III : When two different balls are chosen, the red ball is returned to the bag. The bags in the balls after second last trial will be (red, black) or (red, red, red). In both cases, there would be a red ball in the bag, Hence, the probability of red ball in bag is 1 .