An urn A contains 3 white and 5 black balls. Another urn B contains 6 white and 8 black balls. A ball is picked from A at randomly and then transferred to B. Then a ball is picked at random from B. The probability that it is a white ball is

Let A₁, A₂ be the events of picking events white ball, black ball respectively from bag A. Then $P\left(A_1\right)=3/8,P\left(A_2\right)=5/8$

Let E be the event of picking a white ball from bag B after a ball is transformed from bag A to bag B 

Then $P\left(E/A_1\right)=7/15,P\left(E\mid A_2\right)=6/15$

$\therefore P\left(E\right)=P\left(A_1\right)P\left(E\mid A_1\right)+P\left(A_2\right)P\left(E\mid A_2\right)=\frac{3}{8}\times \frac{7}{15}+\frac{5}{8}\times \frac{6}{15}=\frac{51}{120}=\frac{17}{40}$