There are two bags P and Q. Bag P contains 5 Yellow and 6 Green balls while bag Q contains 6 Yellow and 5 Green balls. As a part of an experiment, a fair dice is rolled. If the face 2 or 5 turns up, a Green ball is taken from bag P and is then placed into bag Q. If any other face turns up, a Green ball is taken from bag Q and is then placed into bag P. The experiment is performed twice. What is the probability that total number of balls in bag P is not more than that in Bag Q after performing the experiments?
Bag P will not have more number of balls than bag Q if we exclude the case where both the experiments result in placing Green balls in bag P. So, probability of bag P having total number of balls not more than Bag Q = 1 – Probability of getting (1 or 3 or 4 or 6) during both the experiments = 1 – 4/6 × 4/6 = 5/9
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