An urn contains 10 white and 3 black balls.Another urn contains 3 white and 5 black balls.Two balls are drawn from the first urn and put into the second urn and then a ball is drawn from the second urn.Find the probability that ball drawn from 2nd urn is white.

Explanation

Let `E_{1}=2` white balls put from 1 to 2


`{E}_{2}=2` black balls put from 1 to 2


`E_{3}=1` white and 1 black ball put from 1 to 2


`{A}=` white ball choosen from urn 2


`P(E_{1})=frac{{ }^{10} C_{2}}{{ }^{13} C_{2}}, P(E_{2})=frac{{ }^{3} C_{2}}{{ }^{13} C_{2}}, P(E_{3})=frac{{ }^{10} C_{1} times{ }^{3} C_{1}}{{ }^{13} C_{2}}`



`{P}({A} / {E}_{1})=frac{{ }^{5} {C}_{1}}{{ }^{10} {C}_{1}} `


`{P}({A} / {E}_{3})=frac{{ }^{4} {C}_{1}}{{ }^{10} {C}_{1}}`


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