2021 April MIMC 10 Problems/Problem 25

Suppose that a researcher hosts an experiment. He tosses an equilateral triangle with area $\sqrt{3}$ $cm^2$ onto a plane that has a strip every $1$ $cm$ horizontally. Find the expected number of intersections of the strips and the sides of the equilateral triangle.

$\textbf{(A)} ~4 \qquad\textbf{(B)} ~\frac{12}{\pi} \qquad\textbf{(C)} ~\frac{2+3\sqrt{3}}{2} \qquad\textbf{(D)} ~\frac{4+\sqrt{3}}{2} \qquad\textbf{(E)} ~\frac{12+4\sqrt{2}-2\sqrt{3}}{4}\qquad$

Solution

To be Released on April 26th.

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2021 April MIMC 10 Problems/Problem 25

Solution