Dice $A$ has $4$ red and $2$ white faces whereas dice $B$ has $3$ red and $3$ white faces. A coin is tossed once, if it falls head then the game continues by throwing the dice $A$ and if it falls tail then the dice $B$ is to be used. If red turns up at first $3$ throws, then the probability that dice A is being used is

• A

  $\frac{7}{37}$
• Correct answer
  B

  $\frac{64}{91}$
• C

  $\frac{9}{41}$
• D

  $\frac{27}{35}$

Hence, the correct answer is option: 'B'.