Any student who misspelled any word on _ paper was given an f.
a) his b) their

The best answer choice is:  [A]:  "his" .

Note:  The best answer, GIVEN THE TWO (2) answer choices; would be: 
      [A]: "his" ; since "their" would INCORRECLY indicate the "plural" form of subject-verb agreement.

Better options would include: "one's", or "his or her".  
    {or even rephrasing the sentence}.

 But the "best" option is:  [A]:  "his" ;  —  NOT:  [B]:  "their" .