Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn…

Bag A contains $\displaystyle 2$ white, $\displaystyle 1$ black and $\displaystyle 3$ red balls and bag B contains $\displaystyle 3$ black, $\displaystyle 2$ red and n white balls. One bag is chosen at random and $\displaystyle 2$ balls drawn from it at random, are found to be $\displaystyle 1$ red and $\displaystyle 1$ black. If the probability that both balls come from Bag A is $\displaystyle \frac{6}{11}$, then n is equal to \_\_\_\_.