Question 1194840
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An urn contains 5 white and 7 black balls. Another urn contains 3 white and 9 black balls. 
If one ball from the first urn is selected at random and is transferred to the second urn, 
what is the probability that the ball drawn from the second urn gives a black?
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<pre>
First urn is (5W,7B) at the beginning, while second urn is (3W,9B).


After the transfer a ball from the first urn to the second urn, 

                  - the 2nd urn becomes (4W,9B)  with the probability of 5/(5+7) = 5/12,
                        if a white ball is transferred from the 1st urn,
or
                  - the 2nd urn becomes (3W,10B) with the probability of 7/(5+7) = 7/12,
                        if a black ball is transferred from the 1st urn.


Hence, the probability to draw a black ball from the second urn is

    {{{(5/12)*(9/13) + (7/12)*(10/13)}}} = {{{45/156 + 70/156}}} = {{{(45+70)/156}}} = {{{115/156}}}.    <U>ANSWER</U>
</pre>

Solved.