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\(\begin{align*} \Pr(X_1 + X_2 + X_3 \geq 7 | X_1 = 2) \amp = \frac{\Pr(X_1 + X_2 + X_3 \geq 7, X_1 = 2)}{\Pr(X_1 = 2)} \\ \amp = \frac{\Pr(X_2 + X_3 \geq 5) \Pr(X_1 = 2)}{\Pr(X_1 = 2)} \\ \amp = \Pr(X_2 + X_3 \geq 5) \\ \amp = \Pr(Y \geq 5) \end{align*}\)
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