There are  urns labeled X, Y, and Z.

Urn X contains 4 red balls and 3 black balls.
Urn Y contains 5 red balls and 4 black balls.
Urn Z contains 4 red balls and 4 black balls.

One ball is drawn from each of the urns. What is the probability that,
of the balls drawn, are red and is black?

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The picks of ball of either Red or Black in X, Y, Z urns are independent events.

There are 3 possible independent picks for the outcome of 2 Red and 1 Black balls:

                                        4     5     1     20
P(X=red) and P(Y=red) and P(Z=black) = --- * --- * --- =  ---
                                        7     9     2	  126

                                        4     4     1     16
P(X=red) and P(Y=black) and P(Z=red) = --- * --- * --- =  ---
                                        7     9     2     126


                                        3     5     1     15
P(X=black) and P(Y=red) and P(Z=red) = --- * --- * --- =  ---
                                        7     9     2     126


20      16      15      51     17
--   +  ---  +  ---  =  --- =  ---
126     126     126     126    42