Investment Banking Quant Interview Puzzles

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Question 1 P and Q are two points chosen at random between 0 and 1. What is the probability that ratio p/q lies between 1 and 2?

Geometrically it will be a square on side 1 on p and q axis.

Geometrically it will be set of 2 lines in p and q axis.

It will be equal to the area of triangle (0,0), (1,1) and (1,0.5)

Probability = 1/4

Question 2 Two friends make an evening visit to Corner House for DBC. Each arrives at a random time between 5:00 and 5:30 pm. Each one of them stays for exactly 30 minutes. On any one given evening, what is the probability that the two friend will meet at Corner House ?

We can calculate the ratio of shaded area inside the grid of (60*60) and of the grid, that will give us the required probability.