Today I have been asked the following question: If we have two coins which one is double headed, and we toss a coin and is head, what is the probability for the other side to be a tail?

I will write the correct answer and why in comments.

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June 23, 2013 at 9:24 am

We have two coins Double Head (D) and Normal (N). The question is what is the probability of seeing the normal coin if we have already seen a head.

P(N|H) = P(H|N).P(N)/P(H)

P(H|N) = If we know the coin is normal, what is the probability of getting a head? 1/2

P(N) = 1/2

P(H) = What is the probability of getting a head with no additional Knowledge? 3/4.

P(N|H) = 1/3