P("choose fair coin") = 24/25
P("choose unfair coin") = 1/25
P("6H under the condition fair coin")\(= 2^{-6} = \frac{1}{64}\)
P("6H under the condition unfair coin")=1
let a=P("choose fair coin") * P("6H under the condition fair coin") = 24/25 * 1/64
let b=P("choose unfair coin") * P("6H under the condition unfair coin") = 1/25
\(\frac{b}{a+b} = \frac{m}{n} = \frac{8}{11}\)
m+n=19