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Hard · Conditional Expected Value · Quant Trader interview question · probability, expected-value, mental-math, conditional-expectation
You are trading a novel contract that pays based on the sequence of coin flips. Consider a fair coin (50% heads, 50% tails). How many expected flips does it take to observe the sequence 'HH' (Heads then Heads), compared to the sequence 'HT' (Heads then Tails)? What is the difference in the expected number of flips between observing the sequence HH and observing the sequence HT? Express your answer as a positive number. For example, if it takes on average 10 flips to see 'HH' and 8 flips to see