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You throw 1000 darts. Each one has a 50% chance to score. For the first 500 darts each is worth 1 point, for the second 500 darts each is worth 3 points. If you score 1500 points. Most likely how many 3point darts have you scored.
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Quantitative Researcher

Interviewed at Jane Street

4.4
Aug 9, 2013

You throw 1000 darts. Each one has a 50% chance to score. For the first 500 darts each is worth 1 point, for the second 500 darts each is worth 3 points. If you score 1500 points. Most likely how many 3point darts have you scored.

Unfair coin with P(H) = 1/3 and P(T) = 2/3. a) How to make an event with 50% probability? b) Expected number of flips until a realization occurs? c) Can you create a strategy to reduce the number of flips necessary? d) Can you create a strategy to reduce the number of flips necessary for an unfair coin with any bias?
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Quant

Interviewed at Jane Street

4.4
Apr 1, 2012

Unfair coin with P(H) = 1/3 and P(T) = 2/3. a) How to make an event with 50% probability? b) Expected number of flips until a realization occurs? c) Can you create a strategy to reduce the number of flips necessary? d) Can you create a strategy to reduce the number of flips necessary for an unfair coin with any bias?

You are given an array that represents bills in certain currency (For example 1, 2, 5, 10) and an amount, for example 17. You should output the number of possible combinations of bills that sum to the given amount. For example, {10, 5, 2} is valid combination, {10, 5, 1 ,1} also. I did not ask questions like does the order of bills matter, i.e. is {10, 5, 2} same as {2, 10, 5}.
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Software Engineer

Interviewed at Google

4.4
Mar 22, 2012

You are given an array that represents bills in certain currency (For example 1, 2, 5, 10) and an amount, for example 17. You should output the number of possible combinations of bills that sum to the given amount. For example, {10, 5, 2} is valid combination, {10, 5, 1 ,1} also. I did not ask questions like does the order of bills matter, i.e. is {10, 5, 2} same as {2, 10, 5}.

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