Step 1: Read the statements.
Statement I: Down's syndrome is caused by absence of one X-chromosome. Statement II: Turner's syndrome is caused by an extra copy of chromosomes.
Step 2: Recall aneuploidy.
Aneuploid disorders arise from gain or loss of chromosomes due to non-disjunction during cell division.
Step 3: Recall Down's syndrome.
Down's syndrome is caused by an extra copy of autosome 21 (Trisomy 21), not by losing an X chromosome.
Step 4: Judge Statement I.
Since Down's is a gain of chromosome 21 and not loss of an X, Statement I is incorrect.
Step 5: Recall Turner's syndrome.
Turner's syndrome is caused by the absence of one X chromosome, giving an $XO$ (45 chromosomes) karyotype, which is a loss, not a gain.
Step 6: Judge Statement II and conclude.
Since Turner's is a loss and not an extra copy, Statement II is also incorrect. Both statements are incorrect, which is option (3).
\[ \boxed{\text{Both Statement I and Statement II are incorrect}} \]