Madison Tyler Holdings Interview Question: We play a game. You flip two ... | Glassdoor

Interview Question

Trading Analyst Interview Los Angeles, CA

We play a game. You flip two coins, if you get both heads I

  give you $1. If you get both tails you flip again. If you get one of each, I pay you nothing. What's the expected value of this game?
coins, coin, expected value, coin flips

Interview Answer

5 Answers


Dismiss TT since it is not part of the sample space (ie there is no outcome from it)
You are twice as likely to get one of each (H-T or T-H) versus getting both heads

(2/3)($1) + (1/3)(0) = 66.7 cents

Interview Candidate on Aug 17, 2011




kerzane on Oct 18, 2011

interviewer told me .667 is correct

Kerzane is wrong on Oct 24, 2011

HT and TH add up to 1/2 of the probability with zero payout. HH is 1/4 probability with $1 payout. TT results in a "reset" so we can disregard. After we normalize the probabilities, we get: E[payout]= (1/3)*$1 + (2/3)*$0 = $0.33

Kerzane is right on Oct 28, 2011

You can also see it a geometric series.
By writing E=0.25x1+0.5x0+0.25xE, Kerzane could as well have written
E?0.25x1 + 0.5x0 + 0.25x(0.25x1 + 0.5x0 + 0.25x(0.25x1 + 0.5x0 + 0.25x(....)))
This is quite simply the geometric sum: (n-> infinity) E=0.25 + 0.25^2 + 0.25^3....0.25^n
which is equal to 0.25/(1-0.25) = 0.25/0.75 = 1/3 or 0.333

Kerzane is really right on Dec 7, 2011

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