she travels to Nashville;

she is on her way to Nashville, given that she is flying.

attempt to set up the problem using a tree diagram and/or an equation, with the unknown $x$     M1

$\frac{4}{5}x + \frac{2}{3}(1 - x) = \frac{{13}}{{18}}$     A1

$\frac{{4x}}{5} - \frac{{2x}}{3} = \frac{{13}}{{18}} - \frac{2}{3}$

$\frac{{2x}}{{15}} = \frac{1}{{18}}$

$x = \frac{5}{{12}}$     A1

[3 marks]

attempt to set up the problem using conditional probability     M1

EITHER

$\frac{{\frac{5}{{12}} \times \frac{1}{5}}}{{1 - \frac{{13}}{{18}}}}$     A1

OR

$\frac{{\frac{5}{{12}} \times \frac{1}{5}}}{{\frac{1}{{12}} + \frac{7}{{36}}}}$     A1

THEN

$= \frac{3}{{10}}$     A1

[3 marks]

Total [6 marks]