B: Bised coin
F: Fair coin
Four tails: T
We should find P( B | T )
Bayes theorem works fine here,
Probability of choosing coin with no tosses
P(B)=1/4
p(F)=3/4
Probability of of 4 tails in each case,
P( T | B )=1 (always tails)
P( T | F)=1/16
P(B | T)= P( T | B) P(B) / P(B)P(T | B ) + P(F) P(T | F)
=16/19