The formulas for conditional probability are:
[tex]P(A\cap B')=P(A)\cdot P(B'|A)[/tex]
[tex]P(A\cap B')=P(B')\cdot P(A|B')[/tex].
Since [tex]P(A\cap B')= \frac{1}{6} [/tex] and [tex]p(B')= \frac{7}{18} [/tex], you have the equation [tex] \frac{1}{6} = \frac{7}{18} \cdot P(A|B')[/tex].
Therefore, [tex]P(A|B')= \frac{1}{6} : \frac{7}{18} =\frac{1}{6} \cdot \frac{18}{7} = \frac{3}{7} [/tex].
Answer: The correct choice is D.
