1) Explanation

Let's break down the sentence to understand the context and the meaning required for the blank:
- "Hannah and Louise appear to refute the hypothesis that the shared genetic code of identical twins creates duplicate personalities,..."
- This sets up the core idea: the twins have different personalities, despite being genetically identical, thus refuting the hypothesis.
- "...as Hannah has never been inclined to stray far from her small farming town in Nebraska, while Louise has a $\qquad$ for travel and often derides her sister's provincialism."
- "Hannah has never been inclined to stray far from her small farming town": This describes Hannah's personality as home-loving, perhaps sedentary or rooted.
- "while": This signals a direct contrast between Hannah and Louise.
- "Louise has a $\qquad$ for travel": This means Louise has a strong liking, inclination, or tendency towards travel.
- "and often derides her sister's provincialism": "Provincialism" means a narrow, restricted, or unsophisticated outlook characteristic of people from a small, isolated area. Louise deriding this reinforces her own contrasting personality (worldly, adventurous).

Therefore, the blank needs words that mean a strong liking, inclination, or tendency.

Let's evaluate the given options:
- A. premonition: A strong feeling that something is about to happen, especially something unpleasant. This is irrelevant to a liking for travel.
- B. penance: Voluntary self-punishment inflicted as an outward expression of repentance for wrongdoing. This is irrelevant.
- C. precedent: An earlier event or action that is regarded as an example or guide to be considered in subsequent similar circumstances. This is irrelevant.
- D. prerogative: A right or privilege exclusive to a particular individual or class. This is irrelevant to a liking or tendency.
- E. penchant: A strong or habitual liking for something or tendency to do something. This perfectly fits "a liking for travel."
- F. proclivity: A tendency to choose or do something regularly; an inclination or predisposition toward a particular thing. This is a strong synonym for "penchant" and also perfectly fits "a tendency for travel."

Conclusion:
The sentence highlights the contrasting personalities of the twins, with Louise having a strong inclination towards travel. Both "penchant" and "proclivity" accurately convey this meaning.

The final answer is $\(\mathrm{E}, \mathrm{F}\)$.