Shortest of three uniform gum sticks

A faulty dispenser gives three gum sticks whose lengths are independent and uniform on $[0,3]$. You receive the shortest one. What is the probability that your stick's length is between 1 and 2?

$7/27$. The minimum exceeds $t$ when all three do: $\left(\tfrac{3-t}{3}\right)^3$. So $P(1<\min<2)=\left(\tfrac23\right)^3-\left(\tfrac13\right)^3=\tfrac{7}{27}$.