Final answer:
Option 2: 'I believe I am invincible and nothing bad can happen to me.' is the statement that indicates a personal fable, as it demonstrates a belief in one's invulnerability and uniqueness, which is characteristic of adolescent egocentrism.
Step-by-step explanation:
A student has asked which of Ethan's statements indicates a personal fable. In developmental psychology, a personal fable is a belief held by adolescents that they are unique, special, and immune to harm that could befall others. This concept is part of a larger framework of adolescent egocentrism identified by David Elkind.
Given the options provided, Option 2: "I believe I am invincible and nothing bad can happen to me." is an indication of a personal fable. This statement implies that Ethan feels immune to the consequences and dangers that others might face, which fits the definition of a personal fable.
This sense of invulnerability is a common aspect of adolescent thinking and differs from the other options because it is directly linked to an overestimation of one's uniqueness and a dismissal of risk.
The other options do not reflect a personal fable. Option 1 reflects the imaginary audience, another concept related to adolescent egocentrism, while Options 3 and 4 describe more general thinking and behavior patterns not specific to a personal fable.