Abag contains 5 white and 3 black balls. another bag contains 4 white and 5 black balls. from any one of these two bags, two balls are drawn at random at one time. what is the probability that the two drawn balls are white and black?

From bag 1, to get a white and then a black, or a black then a white,

the prob is (5/8 x 3/7) + (3/8 x 5/7) {NB NO replacement, ball is not put back in bag}

for bag 2, the same prob is: (4/9 x 5/8) + (5/9 x 4/8)
 
totalling this and assuming it's 50:50 that one bag will be chosen to the other,
 
the odds are 1/2( (5/8 x 3/7) + (3/8 x 5/7)) + 1/2 ( (4/9 x 5/8) + (5/9 x 4/8)) =

0.5456
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