A student is chosen at random from a class. Each student is equally likely to be chosen.

Which of the following conditions is/are necessary for the probability that the student wears glasses to equal $\frac{4}{15}$ ?

I Exactly 11 students in the class do not wear glasses.

II The number of students in the class is divisible by 3.

III The class contains 30 students, and 8 of them wear glasses.

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