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A bag $A$ contains $4$ green and $6$ red balls. Another bag $B$ contains $3$ green and $4$ red balls. If one ball is drawn from each bag, find the probability that both are green:
  • A$\frac{13}{70}$
  • B$\frac{1}{4}$
  • C$\frac{6}{35}$
  • D$\frac{8}{35}$
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