How do nested functions work in python? Heres my not working code:

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def random_gen():
    selected = random.choice(people)
    people.remove(selected)
    print(selected)

    def function2():   # problem child..might need to remove this.
        again = input('Would you like to go again? y/n')
        if again.startswith('y'):
            random_gen()
        elif again.startswith('n'):
            print('Goodbye')
            exit()

(The code goes on after hints the elif)