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Madison Tyler Holdings Trading Analyst Interview Question

I interviewed in Sydney (Australia) and was asked:
"There are 5 coins on a table. One of them has a heads on both sides. If you pick up one of the coins and flip it 5 times and get heads each time what is the probability that you have picked up the double sided coin?"
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0
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8/9
- Interview Candidate on May 24, 2011 Flag Response
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Total possibilities that lead to 5 heads in 5 flips:

chose the double head coin + 2^5 possible results = 32
plus
chose any of 4 other coins and flipped HHHHH = 4

So the total number of states that lead to 5 heads is 36. In 32 of them, you chose the double-headed coin, so your chances of having picked the double headed coin, given that you flipped 5 heads is

32/36 = 8/9
- fizixgeek on Feb 14, 2012 Flag Response
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There is only one double sided coin. So the probability is equal to the probability of getting the double sided coin and flipping five heads which is (1/5)*1 plus the probability of getting one of the other four normal coins and flipping 5 heads which is (4/5)*(1/2)^5
- Anonymous on Jun 13, 2014 Flag Response

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