you pull out 2 balls, one after another, from a bag which has 20 blue and 13 red balls in total. if the balls are of similar colour, then the balls are replaced with a blue ball, however, if the balls are of different colours, then a red ball is used to replace them. once the balls are taken out of the bag, they are not placed back in the bag, and thus the number of balls keep reducing. determine the colour of last ball left in the bag.
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There are 3 possible cases of removing the two balls…
a) If we take off 1 RED and 1 BLUE, in fact we will take off 1 BLUE
b)If we take off 2 RED, in fact we will take off 2 RED (and add 1 BLUE)
c) If we take off 2 BLUE, in fact we will take off 1 BLUE
So In case of (a) or (c), we are only removing one blue ball, but we always take off red balls two by two.
1) 20 Blue, 14 Red balls
If there are 14 (even) number of red balls, we can not have one single red ball left in the bag, so the last ball will be blue.
2) 20 Blue, 13 Red balls
Now as the no. of red balls is odd, there will be one single red ball in the bag with other blue balls, and whenever we remove 1 red and 1 blue ball, we end up taking off only the blue ball. So the red ball will be the last ball in the bag.
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