Thick Coin - QuantGuide

Questions Mental Math Discussion Pricing

Thick Coin

Hard

Probability

Let the radius of a penny be

1

. Assume that the thickness of the penny is non-negligible so that a flipped penny can land on its side. Find the thickness of the penny that, when flipped, has a

\dfrac{1}{3}

chance of landing on its side. The answer is in the form

\dfrac{1}{\sqrt{k}}

for an integer

k

. Find

k

\textbf{Note:}

There is no definite answer for this question. Take the approach of inscribing the penny in a sphere.

Notes

Hint

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Thick Coin

Hard

Probability

Let the radius of a penny be

1

. Assume that the thickness of the penny is non-negligible so that a flipped penny can land on its side. Find the thickness of the penny that, when flipped, has a

\dfrac{1}{3}

chance of landing on its side. The answer is in the form

\dfrac{1}{\sqrt{k}}

for an integer

k

. Find

k

\textbf{Note:}

There is no definite answer for this question. Take the approach of inscribing the penny in a sphere.

Notes

Hint