# Maximum of three random variables - what's wrong with my method?

Let $X_1, X_2$, and $X_3$ be three independent, identically distributed random variables each with density function $f(x) = 3x^2$ for $0 \leq x \leq 1$. Let $Y = \max\{X_1,X_2,X_3\}$. Find $P[Y>1/2]$.

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