conditional probability: we are trying to find P(unfair coin given that we got 10 heads). Using bayes rule, the probability is equal to P(unfair coin and 10 heads)/P(10 heads).
The probability of getting an unfair coin and 10 heads is 1/100, as there is a 1/100 chance of getting an unfair coin, and that is guaranteed to give 10 heads in a row.
The probability of getting 10 heads is p(normal + 10 heads) + p(rigged coin + 10 heads), which is 99/100 * 1/1024 + 1/100*1, which is (99+1024)/(100*1024).
Dividing, we get that the probability is 1/100 * (100*1024/(99+1024), which is 1024/1123!
(All that comp math did pay off somewhere lmao).
@viralv4953