Help the seasoned traveler give advice to their extremely unprepared friend.

Since you are going to Antarctica, you should pack a very warm coat. Also, you probably shouldn't expect to find many tropical beaches there.

Since you are going to Antarctica, you should pack a very warm coat.

"Should" is a modal verb, which means it must be followed directly by a bare infinitive (the dictionary form of the verb, without "to").

Also, you probably shouldn't expect to find many tropical beaches there.

The correct negative form is "shouldn't" (or "should not") plus the base verb. Modal verbs never take an "-s" ending, even for third-person subjects, and the word "not" comes directly after "should".