Probablity

[Guest]

Urn A contains 3 white balls and 4 black balls, whereas urn B contain 4 white
balls and 6 black balls. A ball is drawn at random from urn B and placed in urn A. A
ball is then drawn from urn A. It happens to be black. What is the probability that the
ball transferred was black?

[shyamjayakannan]

[tex]\displaystyle\frac{\displaystyle\frac{6}{10}\times\frac{5}{8}}{\displaystyle\frac{6}{10}\times\frac{5}{8}+\frac{4}{10}\times\frac{4}{8}}=\frac{30}{30+16}=\boxed{\frac{15}{23}}[/tex]