HMM for solving given coin output

Question

I have got this assignment question on HMM and I have solved it. I would like to know if I am correct. The problem is:

Suppose a dishonest dealer has two coins, one fair and one biased; the biased coin has heads probability 1/4. Assume that the dealer never switches the coins. Which coin is more likely to have generated the sequence HTTTHHHTTTTHTHHTT? It may be useful to know that log₂(3) = 1.585

I calculated the P for fair coin and biased coin. The P for fair coin is 7.6*10^-6 where as P for biased coin is 3.43*10^-6. I didn't use log term, which can be used if I solve it the other way. So, I concluded that it is more likely that the given sequence is generated by a fair coin.

Am I right?

Any help is greatly appreciated.