quant interview
Expected Rolls to See Every Number on a Die
A fair 6-sided die is rolled until you get every number on the die. The order in which the numbers appear does not matter.
What is the expected number of die rolls?
Expected Tosses for Three Consecutive Heads
A fair coin is tossed repeatedly until three consecutive tosses are heads. What is the expected number of coin tosses?
Grid Path Probability: Through the Center to Cheese
A mouse starts at the bottom left corner of a 
grid. At each step, he can only move RIGHT or UP, moving on the grid lines. He wants to get to the upper right corner, where the cheese is located.
All unique paths are equally likely to be chosen. What’s the probability that he will pass through the center of the grid?
Read More »Grid Path Probability: Through the Center to Cheese
Investment Strategy for a Highly Volatile Stock
For a given stock, you are certain that for the next 100 days, it will move either 10% up or 10% down each day. You can invest now, but if you choose to do so, you have to hold it for the entire 100 days. Would you do so?
Expected Sum of Distances in a Triangle
In a triangle with sides 45, 60, respectively 75, what is the expected sum of distances from a point to its sides?
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