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There are
6 black counters and 4 white counters in bag A
7 black counters and 3 white counters in bag B
5 black counters and 5 white counters in bag C
Bernie takes at random a counter from bag A and puts the counter in bag B.
He then takes at random a counter from bag B and puts the counter in bag C.
Find the probability that there are now more black counters than white counters in bag C.