Belvedere Trading interview questions

Quantitative Trader Intern · Interview · Expected value · reported by a candidate

18 people of different heights sit in a random order around a circle.

1. What is the expected number who are taller than both their neighbours?
   Answer and worked solution

   Answer: 6

   Key idea. Linearity over the 18 positions.

   1. Each person is the tallest of themselves and their two neighbours with probability 1/3.
   2. E = 18 × 1/3 = 6.

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Quantitative Trading intern · Interview · Game theory · reported by a candidate

Three dice: red has faces 2, 6, 7; green has 1, 5, 12; blue has 3, 4, 8 (each face equally likely). Two players each roll a die and the higher number wins. Which die would you choose?

1. First: what is the probability that red beats green?
   Answer and worked solution

   Answer: 5/9 ≈ 0.55556

   Key idea. Count the 9 equally likely face pairs.

   1. Red 2 beats green's 1 only. Red 6 and red 7 each beat 1 and 5.
   2. Wins: 1 + 2 + 2 = 5 of 9: 5/9.
   3. Similarly green beats blue 5/9 and blue beats red 5/9: the dice are non-transitive.

   Check. So there's no best die. Let your opponent choose first, then pick the die that beats theirs.

   Trap. Picking the die with the highest face, or the highest average (all three average 5).

Interviewers may push further: Check green against blue and blue against red. So which die should you pick, and when?

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Trading intern · Interview · Probability · reported by a candidate

100 passengers board a full plane one at a time. The first has lost their boarding pass and sits in a random seat.

The usual version: 100 seats, one per passenger. The first passenger sits in a random seat; everyone after takes their own seat if it's free and a random free seat otherwise.

1. What is the probability that the last passenger sits in their own seat?
   Answer and worked solution

   Answer: 0.5

   Key idea. Only two seats matter: the first passenger's and the last passenger's.

   1. Every displaced passenger picks randomly among the free seats, so at each such moment those two seats are equally likely to be taken.
   2. As soon as one of them is taken, the outcome is settled: the first passenger's seat means everyone else, including the last, gets their own seat.
   3. By symmetry: P = ½.

   Check. It doesn't depend on the number of seats (for 2 or more).

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Trading Analyst intern · Interview · Mental maths · reported by a candidate

Mental arithmetic reported from Belvedere trading-intern interviews.

1. (a) 3/32 as a decimal
   Answer and worked solution

   Answer: 0.09375

   Key idea. Know 1/32.

   1. 1/32 = 0.03125; × 3 = 0.09375.
2. (b) 38 × 42
   Answer and worked solution

   Answer: 1596

   Key idea. Difference of squares.

   1. (40 − 2)(40 + 2) = 1600 − 4 = 1596.
3. (c) 62 × 74
   Answer and worked solution

   Answer: 4588

   Key idea. Split one factor.

   1. 62 × 70 = 4340; 62 × 4 = 248.
   2. 4588.

   Check. Ends in 8 (2 × 4).

Source: Wall Street Oasis: Belvedere Trading interview reports · Try it in the app →