A dishonest gambler has a box containing 10 dice which all look the same. However there are actually three types of dice.  

There are 6 dice of type $A$ which are fair dice with $\operatorname*{Pr}(6\mid A)=1/6$ (where $\operatorname*{Pr}(6\mid A)$ is the probability of getting a 6 in a throw of a type $A$ die). There are 2 dice of type $B$ which are biassed with $\operatorname*{Pr}(6\mid B)=0.8$ .There are 2 dice of type $C$ which are biassed with $\operatorname*{Pr}(6\mid C)=0.04$ .  

The gambler takes a die from the box at random and rolls it. Find the conditional probability that it is of type $B$ given that it gives a 6. 