Jane Street–styleTraderAssistant TraderQuestion #194
1. A larger cube is made up of 27 smaller cubes. If the exterior of the larger cube is painted red and then a small cube is chosen at random and rolled like a die, what is the probability that no red faces are showing? Given that no red faces are showing, what is the probability that the rolled cube is the center cube (which has no red faces)? 2. If I roll two ten-sided dice, which is more likely: rolling two odd numbers or rolling two even numbers?
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More Jane Street–Style Trader Questions
A car has a uniformly distributed value between 0 and 1000. If you bid less than this value, you get nothing but keep your bid. If you bid more than this value, you can sell the car for 1.5 times the value. What should you bid? The surface of a 3x3 block is painted. The block is split into 27 cubes and one is dropped on the floor. What is the probability that no visible face is painted? If no visible face is painted, what is the probability that it is the center cube?You flip 4 fair coins and receive $1 for each coin that lands heads. What is the expected value of your total winnings?If you roll two dice, and you have the option to roll again and get paid the highest roll, when is it optimal to reroll?What is 2,000,000 minus 2,022?How many digits does 99 raised to the 99th power have?
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