# There are two bags , one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls . A die is cast if the face 1 or 3 turns up a ball is taken out from the first bags and if any other face turns up , a ball is taken from the second bag . the probability of choosing a black ball is

Solutions :    Let $C$ be the bag with $3$ black and $4$ white balls

and $D$  the bag with $4$ black and $3$ white balls .

$\Rightarrow$       $P(B)=P(C)P(\frac{B}{C})+P(D)P(\frac{B}{D})$

$\Rightarrow$       $P(B)=\frac{2}{6}\cdot \frac{3}{7}+\frac{4}{6}\cdot \frac{4}{7}=\frac{11}{21}.$

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