Answer
P(no children or only the husband works) $=\frac{1041}{1700}\approx0.612$
Work Step by Step
The sample space: 1700 married couples. So, N(S) = 1700
According to the marginal distribution (see definition, page 235) of the first row: N(only the husband works) = 425
According to the marginal distribution (see definition, page 235) of the first column: N(no children) = 788
According to the cell in the first row, first column: N(no children and only the husband works) = 172.
P(no children or only the husband works) = P(only the husband works) + P(no children) - P(no children and only the husband works) =
$\frac{N(\text{only the husband works})}{N(S)}+\frac{N(\text{no children})}{N(S)}-\frac{(\text{no children and only the husband works})}{N(S)}=\frac{425}{1700}+\frac{788}{1700}-\frac{172}{1700}=\frac{1041}{1700}\approx0.612$
