Step 1: Read what changes in the person.
The person does not change behaviour or performance. Only the confidence in an existing opinion goes up, because others share it. We must find the term for that.
Step 2: Rule out the terms that need a change in action.
Social facilitation is about doing a task better in front of others. Conformity is about changing what one does or says to fit the group. Neither describes a belief simply feeling more valid. So (1) and (4) are out.
Step 3: Rule out the reasoning error.
Hasty generalization is a faulty step from a few examples to a rule. The person here is not generalizing from samples. So (3) is out.
Step 4: Confirm the remaining term.
The bandwagon effect describes belief getting stronger when it is popular, as if joining a moving crowd. This matches the example, so (2) is right.
Step 5: Put it in plain words.
Think of a person who thinks capital punishment is right and then sees many others agree. The person feels safe and sure, because the crowd seems to prove the view. That feeling of being proved right by the crowd is the bandwagon effect, not a change of action and not a faulty rule drawn from few cases.
Final Answer:
The bandwagon effect fits the situation, so the answer is option (2).\[ \boxed{2} \]