Optiver interview questions

A swim coach must identify her three fastest athletes out of $25$, but the pool has only $5$ lanes and the stopwatch is broken — each heat of $5$ swimmers reveals only their finishing order, never times. Every swimmer performs identically in every heat. What is the minimum number of heats guaranteed to determine the fastest, second-fastest, and third-fastest swimmers?

A table-tennis game is tied $10$–$10$, and from here the winner is the first player to lead by two points. You win each point with probability $\frac{1}{3}$ and your opponent with probability $\frac{2}{3}$, independently. What is the probability that you win the game?

Two contractors submit sealed bids for a job, each bid drawn independently and uniformly from $[0, 1]$ (in millions of dollars). The client always takes the higher bid. What is the expected value of the winning (higher) bid?