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You have 100 coins. 99 are fair and 1 is double sided. You pick a random coin and flip it 10 times and get 10 heads in a row. What is the probability that you picked the double sided coin?

Response / help needed:

Probablity of picking a 1 sided coin = .01

Probability of heads 10 times in a row with an fair coin = .5^(10)

Probability of heads 10 times in a row with an unfair coin (assuming the head is on both sides) = 1

So, i think, according to baye's, the equation should be

.01*1/ (.01*1+ .5^10*.99) = .912

Is that correct?

Also, what would you do if you do not assume heads is on both sides?