Case Ist Let a white ball be transfered from the first bag to the second bag.
The probability of selecting white ball from the first bag is
P1=‌=‌Now, the second bag has 7 white and 8 black balls. The probability of selecting a white ball from the second bag is
P2=‌=‌The probability that both these events take place simultaneously
=P1×P2=‌×‌=‌Case IInd Let a black ball be transfered from the first bag to the second bag.
Its probability is
P3=‌=‌Now, the second bag contains 6 white and 9 black balls.
The probability of drawing a white ball from the second bag is
P4=‌=‌∴ The probability of both these events taking place simultaneously
=P3×P4=‌×‌=‌∴ The required probability
=P1P2+P3P4‌=‌+‌‌=‌=‌