Answer
The events "Mallory" and "Filters" are not independent because $P(Mallory)\ne P(Mallory~|~Filters)$
Work Step by Step
The sample space: 1009 cases. $So, N(S)=1009$
According to the marginal distribution (see page 235) of the fourth row: $N(Mallory)=186$
Using the Empirical Approach (page 258):
$P(Mallory)=\frac{N(Mallory)}{N(S)}=\frac{186}{1009}\approx0.1843$
According to the marginal distribution (see page 235) of the third column: $N(Filters)=120$
According to the cell in the fourth row, third column: $N(Mallory~and~Filters)=40$
$P(Mallory~|~Filters)=\frac{N(Mallory~and~Filters)}{N(Filters)}=\frac{40}{120}=\frac{1}{3}\approx0.3333$
$P(Mallory)\ne P(Mallory~|~Filters)$
The events "Mallory" and "Filters" are not independent (see definition on page 292).