The odds in favor of event A are given as the ratio of the probability of A occurring to the probability of A not occurring:

$$
\(\text { Odds in favor }=\frac{P(A)}{P\left(A^c\right)}=\frac{P(A)}{1-P(A)}\)
$$


Given the odds in favor of arrival are $3: 7$, so:

$$
\(\frac{P(\text { arriving })}{P(\text { not arriving })}=\frac{3}{7}\) .
$$


Let:

$$
\(P(\text { arriving })=p\)
$$

therefore:

$$
\(\frac{p}{1-p}=\frac{3}{7}\)
$$


Cross-multiplied:

$$
\(\begin{gathered}
7 p=3(1-p) \\
7 p=3-3 p \\
7 p+3 p=3 \\
10 p=3 \\
p=\frac{3}{10}
\end{gathered}\)
$$

The probability that the shipment does not arrive is:

$$
\(1-p=1-\frac{3}{10}=\frac{7}{10}\)
$$


Final answer:
C. $\(\frac{7}{10}\)$