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Summer Trader Interview Questions


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Flip a coin until either HHT or HTT appears. Is one more likely to appear first? If so, which one and with what probability?

13 Answers

Let A be the event that HTT comes before HHT. P{A} = P{A|H}P{H} + P{A|T}P{T} = .5P{A|H} + .5P{A|T} P{A|T} = P{A} therefore, P{A|H} = P{A|T} P{A|H} = P{A|HH}P{H} + P{A|HT}P{T} = (0)(.5) + P{A|HT}(.5) Therefore, 2P{A|H} = P{A|HT} P{A|HT} = P{A|HTT}P{T} + P{A|HTH}P{H} = (1)(.5) + P{A|H}(.5) 2P{A|H} = .5 + P{A|H}(.5) P{A|H} = 1/3 and P{A|H} = P{A}, therefore, P{A} = 1/3 So, HHT is more likely to appear first and it appears first 2/3 of the time.

P{A|H} = P{A|HH}P{H} + P{A|HT}P{T} = (0)(.5) + P{A|HT}(.5) Need help - - why is P{A|HH} = 0 ?

P(A|HH) = 0 because after a sequence of consecutive heads, you can no longer achieve HTT. The moment you get a tail, you will have the sequence HHT. This the reason HHT is more likely to occur first than HTT.

How many digits are there in 2^50?

5 Answers

A survey is given to all passengers on a number of different planes. The survey asks each person how full their plane was. The people answer honestly. If 50% of people claim that their plane was 80% full, while the other 50% claim that their plane was 20% full, how full was the average plane?

2 Answers

"Why do you want to work in finance." Find a way to bet on individual games in the NBA finals such that no matter the outcome of each game and no matter the number of games to the end of the tournament, you win exactly $100 if your preferred team wins and lost exactly $100 if your preferred team loses. The NBA finals is best out of 7 (4 wins needed to win) so the tournament may terminate at the end of the 4th, 5th, 6th, or 7th rounds. And then questions at their regional office - one game theory question, several questions about minimizing risk or finding expected return of a game.

tech: meanings of singular value, static key words, min stack fit: right or wrong, do you like risk, personalities for trading

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