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I have a cube made up of 27 smaller cubes. I paint the outside of the cube red! I take a random cube and roll it. What is the probability no red faces are showing? Given that I roll no red, what is the probability that the cube is the center cube, with no red faces? I roll two ten sided die. Which is more likely, that I roll two odd numbers, or two even numbers?
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Assistant Trader

Interviewed at Jane Street

4.4★
Mar 30, 2015

I have a cube made up of 27 smaller cubes. I paint the outside of the cube red! I take a random cube and roll it. What is the probability no red faces are showing? Given that I roll no red, what is the probability that the cube is the center cube, with no red faces? I roll two ten sided die. Which is more likely, that I roll two odd numbers, or two even numbers?

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