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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 random and then transferred to B. Then a ball is picked at random from B. The probability that it is a white ball is :

$\begin {array} {1 1} (1)\;\frac{14}{40} & \quad (2)\;\frac{15}{40} \\ (3)\;\frac{16}{40} & \quad (4)\;\frac{17}{40} \end {array}$

$(4)\;\frac{17}{40}$