Final answer:
A student with an entity theory of self is likely to say "I'm just not cut out for chess" after losing competitions, reflecting a belief in fixed abilities.
Step-by-step explanation:
If a student who recently lost several chess matches possesses an entity theory of self, he is most likely to make a statement that reflects a belief in fixed abilities. Among the given options, the statement, "I'm just not cut out for chess," illustrates this mindset.
This viewpoint is grounded in the idea that one's abilities are inherent and unchangeable, rather than something that can be developed through effort or learning. The entity theory of self contrasts with an incremental theory of self, where an individual believes that abilities can be improved through dedication and hard work, which would resonate more with statements like "I need to practice more to improve my skills."